Relevant bibliographies by topics / Infinite intersection of open sets

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Academic literature on the topic 'Infinite intersection of open sets'

Author: Grafiati
Published: 5 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Infinite intersection of open sets"

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DURAND, ARNAUD. "Sets with large intersection and ubiquity." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 1 (2008): 119–44. http://dx.doi.org/10.1017/s0305004107000746.

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AbstractA central problem motivated by Diophantine approximation is to determine the size properties of subsets of$\R^d$ ($d\in\N$)of the formwhere ‖⋅‖ denotes an arbitrary norm,Ia denumerable set, (xi,ri)i∈ Ia family of elements of$\R^d\$× (0, ∞) and ϕ a nonnegative nondecreasing function defined on [0, ∞). We show that ifFId, where Id denotes the identity function, has full Lebesgue measure in a given nonempty open subsetVof$\R^d\$, the setFϕbelongs to a class Gh(V) of sets with large intersection inVwith respect to a given gauge functionh. We establish that this class is closed under counta
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Weihrauch, Klaus, and Tanja Grubba. "Elementary Computable Topology." JUCS - Journal of Universal Computer Science 15, no. (6) (2009): 1381–422. https://doi.org/10.3217/jucs-015-06-1381.

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We revise and extend the foundation of computable topology in the framework of Type-2 theory of effectivity, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. We start from a computable topological space, which is a T0-space with a notation of a base such that intersection is computable, and define a number of multi-representations of the points and of the open, the closed and the compact sets and study their properties and relations. We study computability of b
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Howard, Paul E. "Definitions of compact." Journal of Symbolic Logic 55, no. 2 (1990): 645–55. http://dx.doi.org/10.2307/2274654.

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Several definitions of “compact” for topological spaces have appeared in the literature (see [5]). We will consider the following:Definition. A topological space X is1. Compact(1) if every open cover of X has a finite subcover.2. Compact(2) if every infinite subset E of X has a complete accumulation point (i.e., a point x0 ∈ X such that for every neighborhood U of x0, |E ∩ U| = |E|).3. Compact(3) if there is a subbase S for the topology on X such that every cover of X by members of S has a finite subcover.4. Compact(4) if each nest of closed, nonempty sets has a nonempty intersection.5. Compac
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Živaljević, Boško. "U-meager sets when the cofinality and the coinitiality of U are uncountable." Journal of Symbolic Logic 56, no. 3 (1991): 906–14. http://dx.doi.org/10.2307/2275060.

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AbtractWe prove that every countably determined set C is U-meager if and only if every internal subset A of C is U-meager, provided that the cofinality and coinitiality of the cut U are both uncountable. As a consequence we prove that for such cuts a countably determined set C which intersects every U-monad in at most countably many points is U-meager. That complements a similar result in [KL]. We also give some partial solutions to some open problems from [KL]. We prove that the set , where H is an infinite integer, cannot be expressed as a countable union of countably determined sets each of
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VELDMAN, WIM. "THE FINE STRUCTURE OF THE INTUITIONISTIC BOREL HIERARCHY." Review of Symbolic Logic 2, no. 1 (2009): 30–101. http://dx.doi.org/10.1017/s1755020309090121.

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In intuitionistic analysis, a subset of a Polish space like ℝ or ${\cal N}$ is called positively Borel if and only if it is an open subset of the space or a closed subset of the space or the result of forming either the countable union or the countable intersection of an infinite sequence of (earlier constructed) positively Borel subsets of the space. The operation of taking the complement is absent from this inductive definition, and, in fact, the complement of a positively Borel set is not always positively Borel itself (see Veldman, 2008a). The main result of Veldman (2008a) is that, assumi
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Hajnal, A., and I. Juhász. "Intersection properties of open sets." Topology and its Applications 19, no. 3 (1985): 201–9. http://dx.doi.org/10.1016/0166-8641(85)90001-x.

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Williams, N. H. "An order property for families of sets." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 3 (1988): 294–310. http://dx.doi.org/10.1017/s1446788700032110.

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AbstractWe develop the idea of a θ-ordering (where θ is an infinite cardinal) for a family of infinite sets. A θ-ordering of the family A is a well ordering of A which decomposes A into a union of pairwise disjoint intervals in a special way, which facilitates certain transfinite constructions. We show that several standard combinatorial properties, for instance that of the family A having a θ-transversal, are simple consequences of A possessing a θ-ordering. Most of the paper is devoted to showing that under suitable restrictions, an almost disjoint family will have a θ-ordering. The restrict
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JUHÁSZ, I., ZS NAGY, L. SOUKUP, and Z. SZENTMIKLÓSSY. "Intersection Properties of Open Sets. II." Annals of the New York Academy of Sciences 788, no. 1 General Topol (1996): 147–59. http://dx.doi.org/10.1111/j.1749-6632.1996.tb36806.x.

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González, Osvaldo Guzmán. "P-points, MAD families and Cardinal Invariants." Bulletin of Symbolic Logic 28, no. 2 (2022): 258–60. http://dx.doi.org/10.1017/bsl.2021.24.

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AbstractThe main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal almost disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\math
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Balanda, Kevin P. "Families of partial representing sets." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 2 (1985): 198–206. http://dx.doi.org/10.1017/s1446788700023053.

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AbstractAssume GCH. Let κ, μ, Σ be cardinals, with κ infinite. Let be a family consisting of λ pairwise almost disjoint subsets of Σ each of size κ, whose union is Σ. In this note it is shown that for each μ with 1 ≤ μ ≤min(λ, Σ), there is a “large” almost disjoint family of μ-sized subsets of Σ, each member of having non-empty intersection with at least μ members of the family .
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Books on the topic "Infinite intersection of open sets"

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Wise, Carol. Dragonomics. Yale University Press, 2020. http://dx.doi.org/10.12987/yale/9780300224092.001.0001.

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This book explores the impact of Chinese growth on Latin America since the early 2000s. Some twenty years ago, Chinese entrepreneurs headed to the Western Hemisphere in search of profits and commodities, specifically those that China lacked and that some Latin American countries held in abundance—copper, iron ore, crude oil, fishmeal and soybeans. Focusing largely on Argentina, Brazil, Chile, Costa Rica, Mexico, and Peru, the book traces the evolution of political and economic ties between China and these countries back to the 1950s and explores how more recent and ongoing interaction with Chi
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Book chapters on the topic "Infinite intersection of open sets"

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Gallestey, E., D. Hinrichsen, and A. J. Pritchard. "Spectral value sets of infinite-dimensional systems." In Open Problems in Mathematical Systems and Control Theory. Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0807-8_23.

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Bialostocki, A. "Zero Sum Trees: A Survey of Results and Open Problems." In Finite and Infinite Combinatorics in Sets and Logic. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2080-7_2.

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Bojańczyk, Mikołaj, and Thomas Place. "Regular Languages of Infinite Trees That Are Boolean Combinations of Open Sets." In Automata, Languages, and Programming. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31585-5_13.

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Weller, Martin. "The Rise and Development of Digital Education." In Handbook of Open, Distance and Digital Education. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-2080-6_5.

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AbstractOver the past 25 years, digital education has risen to prominence. It has a direct relationship with open education, which can be considered an umbrella term. In this chapter the rise of digital education is explored through five specific educational technologies. These technologies – the web, Learning Management System (LMS), blogs, social media, and Massive Open Online Courses (MOOCs) – all raise issues of control and ease of use. They also have a direct impact on different aspects of open education, which in turn helps inform their development. This chapter sets out the multiple int
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Weller, Martin. "The Rise and Development of Digital Education." In Handbook of Open, Distance and Digital Education. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0351-9_5-1.

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AbstractOver the past 25 years, digital education has risen to prominence. It has a direct relationship with open education, which can be considered an umbrella term. In this chapter the rise of digital education is explored through five specific educational technologies. These technologies – the web, Learning Management System (LMS), blogs, social media, and Massive Open Online Courses (MOOCs) – all raise issues of control and ease of use. They also have a direct impact on different aspects of open education, which in turn helps inform their development. This chapter sets out the multiple int
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Cimatti, Alessandro, Alberto Griggio, Christopher Johannsen, Kristin Yvonne Rozier, and Stefano Tonetta. "Infinite-State Liveness Checking with rlive." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-98668-0_11.

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Abstract is a recently-proposed SAT-based liveness model checking algorithm that showed remarkable performance compared to other state-of-the-art approaches, both in absolute terms (solving more problems overall than other engines on standard benchmark sets) as well as in relative terms (solving several problems that none of the other engines could solve). proves or disproves properties of the form FGq, by trying to show that $$\lnot q$$ ¬ q can be visited only a finite number of times via an incremental reduction to a sequence of reachability queries. A key factor in the good performance of i
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Wise, Gary L., and Eric B. Hall. "The Counter examples." In Counterexamples in Probability and Real Analysis. Oxford University PressNew York, NY, 1993. http://dx.doi.org/10.1093/oso/9780195070682.003.0001.

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Abstract 1.1.There exists a subset of :R. such that the infimum of the set is greater than the supremum of the set. 1.2 Given any nonzero real number a, there exists a metric on :R. such that a is closer to O than to any other real number. 1.3 There exists an uncountable family of distinct infinite subsets of N such that the intersection of any two distinct sets from this family is finite. 1.4 Given any positive number E, there exists an open subset U of :R. such that U contains each of the rationals, yet the Lebesgue measure of U is less than E. 1.5 There exists a subset S of :R. such that in
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Devi, Dr V. Sutha, and K. Eswari. "LAYER TOPOLOGY." In Futuristic Trends in Contemporary Mathematics & Applications Volume 3 Book 3. Iterative International Publisher, Selfypage Developers Pvt Ltd, 2024. http://dx.doi.org/10.58532/v3bfcm3p9ch2.

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The broad category of whorled patterns, which also comprises a curve that emanates from a point and moves outward as it rounds around the point, contains concentric objects frequently. This ignited us to think over collection of open sets forms a chain where the core open set is non empty and all the other open sets originates from it. This paves us a way to develop the new concept layer topology. Moreover, an attempt has been done to extend this definition in infinite domains like real numbers as standard layer topology, lower limit layer topology and upper limit layer topology in terms of ba
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"Introduction." In The Ancient Sea, edited by Hamish Williams and Ross Clare. Liverpool University Press, 2023. http://dx.doi.org/10.3828/liverpool/9781802077605.003.0001.

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The Introduction sets out the aim of the volume, which are to explore and interpret narrative representations of the ancient sea as utopic (as offering potential, paradise, open roads), as catastrophic (disastrous, chaotic, deathly), and balanced imaginations between these two imagined extremes. The Introduction explains how this study encompasses an array of different ancient narrative genres, including myth, philosophy, historiography and legal, religious, and social narratives. Also explored is their post-classical afterlives in, for example, socio-religious, theatrical, and popular-novelis
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Brix, Tobias J., Malte Berentzen, Ludger Becker, Michael Storck, and Julian Varghese. "Development of a Command Line Interface for the Analysis of Result Sets from Automated Queries to Literature Databases." In Caring is Sharing – Exploiting the Value in Data for Health and Innovation. IOS Press, 2023. http://dx.doi.org/10.3233/shti230095.

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The first step of a systematic review is the identification of publications related to a research question in different literature databases. The quality of the final review is mainly influenced by finding the best search query resulting in high precision and recall. Usually, this process is iterative and requires refining the initial query and comparing the different result sets. Furthermore, result sets of different literature databases must be compared as well. Objective of this work is to develop a command line interface, which supports the automated comparison of result sets of publicatio
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Conference papers on the topic "Infinite intersection of open sets"

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Madan, Reeta, Soni Pathak, R. A. Muneshwar, and K. L. Bondar. "Some properties of the complement of intersection graph derived from topological space using intersection of open sets." In 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS (e-ICMTA-2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0164636.

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Sweigart, D. Blair, Julia Presnell, and Rex Kincaid. "An integer program for Open Locating Dominating sets and its results on the hexagon-triangle infinite grid and other graphs." In 2014 Systems and Information Engineering Design Symposium (SIEDS). IEEE, 2014. http://dx.doi.org/10.1109/sieds.2014.6829887.

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Czechowski, Aleksander, and Frans A. Oliehoek. "Safe Multi-agent Learning via Trapping Regions." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/10.

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One of the main challenges of multi-agent learning lies in establishing convergence of the algorithms, as, in general, a collection of individual, self-serving agents is not guaranteed to converge with their joint policy, when learning concurrently. This is in stark contrast to most single-agent environments, and sets a prohibitive barrier for deployment in practical applications, as it induces uncertainty in long term behavior of the system. In this work, we apply the concept of trapping regions, known from qualitative theory of dynamical systems, to create safety sets in the joint strategy s
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Kumar, Rajeev Ranjan, Sanjoy Kumar Mukherjee, S. K. Biswal, et al. "Field Scale Geo-Mechanical Analysis To Identify Fracture Sweet Spots Within Deccan Trap, Western Onshore, India." In Offshore Technology Conference. OTC, 2021. http://dx.doi.org/10.4043/31206-ms.

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Abstract Hydrocarbon exploration continues to venture into new avenues. This paper elaborates the 3D geomechanical study carried out to identify sweet spots in Deccan Trap Basalts in depth ranging from 500m-1100m in Cambay basin field of India. The main challenge is wide variation in the rock mechanical properties and stress profiles along various azimuths resulting from different tectonic incidents over the geological ages. Several drilling complications and held ups during electro logging in highly deviated wells are also reported. The normal fault tectonic framework has the imprint of two s
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Nanjo, Takashi, Akira Ebitani, Kazuaki Ishikawa, et al. "Automatic Lithology Classification of Cuttings with Deep Learning." In International Petroleum Technology Conference. IPTC, 2023. http://dx.doi.org/10.2523/iptc-22867-ea.

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Abstract Describing cuttings is routine work for wellsite geologists on a drill rig. The time-consuming nature of this analysis and the lack of consistency of the results between different interpreters are the two major concerns for this task. Wellsite geologists spend approximately 70% of their time on cuttings descriptions. In addition, 2 to 3 wellsite geologists are generally assigned to a drilling campaign, and they are replaced at the end of a shift. ML/AI techniques have the potential to solve these issues because of their advantages in prediction speed, objectivity, and consistency. The
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Reports on the topic "Infinite intersection of open sets"

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Lutz, Carsten. PDL with Intersection and Converse is Decidable. Technische Universität Dresden, 2005. http://dx.doi.org/10.25368/2022.148.

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In its many guises and variations, propositional dynamic logic (PDL) plays an important role in various areas of computer science such as databases, artificial intelligence, and computer linguistics. One relevant and powerful variation is ICPDL, the extension of PDL with intersection and converse. Although ICPDL has several interesting applications, its computational properties have never been investigated. In this paper, we prove that ICPDL is decidable by developing a translation to the monadic second order logic of infinite trees. Our result has applications in information logic, descriptio
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Ruttenberg, Judy, Shawna Taylor, Micah Vandegrift, and Cynthia Hudson Vitale. Accelerating Social Impact Research: Libraries at the Intersection of Openness and Community-Engaged Scholarship. Association of Research Libraries, 2022. http://dx.doi.org/10.29242/report.asirjune2022.

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This is the first report of a six-month pilot cohort program from 2021, Accelerating the Social Impact of Research (ASIR). The pilot engaged small teams from eight ARL member libraries who wanted to share strategies to accelerate the adoption and implementation of open-science principles for social-impact research and scholarship. The report, Accelerating Social Impact Research: Libraries at the Intersection of Openness and Community-Engaged Scholarship, sets the context for this confluence, draws examples from the participating members of the cohort, and identifies the opportunities available
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