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Books on the topic 'Generalized topological spaces'

Author: Grafiati

Published: 4 June 2025

Last updated: 7 July 2025

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1

Kunzinger, M. Barrelledness, Baire-like- and (LF)-spaces. Longman Scientific & Technical, 1993.

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2

Molahajloo, Shahla. Pseudo-Differential Operators, Generalized Functions and Asymptotics. Springer Basel, 2013.

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3

Hazod, Wilfried. Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups: Structural Properties and Limit Theorems. Springer Netherlands, 2001.

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4

Francesco, Catoni, ed. The mathematics of Minkowski space-time: With an introduction to commutative hypercomplex numbers. Birkhäuser Verlag, 2008.

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5

Germany) International Conference on p-adic Functional Analysis (13th 2014 Paderborn. Advances in non-Archimedean analysis: 13th International Conference on p-adic Functional Analysis, August 12-16, 2014, University of Paderborn, Paderborn, Germany. Edited by Glöckner Helge 1969 editor, Escassut Alain editor, and Shamseddine Khodr 1966 editor. American Mathematical Society, 2016.

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6

Eijndhoven, Stephanus van, and Johannes de Graaf. Trajectory Spaces, Generalized Functions and Unbounded Operators. Springer London, Limited, 2006.

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7

Damon, James, and Ellen Gasparovic. Medial/Skeletal Linking Structures for Multi-Region Configurations. American Mathematical Society, 2018.

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8

Pears, A. R. Dimension Theory of General Spaces. Cambridge University Press, 2009.

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9

Lectures on Batalin-Vilkovisky Formalism and Its Applications in Topological Quantum Field Theory. American Mathematical Society, 2019.

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10

Pilipovic, Stevan, Shahla Molahajloo, and Joachim Toft. Pseudo-Differential Operators, Generalized Functions and Asymptotics. Springer, 2013.

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11

Molahajloo, Shahla, Stevan Pilipović, Joachim Toft, and M. W. Wong. Pseudo-Differential Operators, Generalized Functions and Asymptotics. Birkhäuser, 2015.

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12

Pseudodifferential Operators Generalized Functions And Asymptotics. Springer Basel, 2013.

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13

Spectral analysis on graph-like spaces. Springer-Verlag, 2012.

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14

Tretkoff, Paula. Topological Invariants and Differential Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0002.

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This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering spaces and some basics of the theory of complex manifolds and Hermitian metrics, including the concept of real manifold. Finally, it provides some general facts about divisors, line bundles, and the first Chern class on a complex manifold X.

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15

Hrushovski, Ehud, and François Loeser. The space of stably dominated types. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0003.

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This chapter introduces the space unit vector V of stably dominated types on a definable set V. It first endows unit vector V with a canonical structure of a (strict) pro-definable set before providing some examples of stably dominated types. It then endows unit vector V with the structure of a definable topological space, and the properties of this definable topology are discussed. It also examines the canonical embedding of V in unit vector V as the set of simple points. An essential feature in the approach used in this chapter is the existence of a canonical extension for a definable function on V to unit vector V. This is considered in the next section where continuity criteria are given. The chapter concludes by describing basic notions of (generalized) paths and homotopies, along with good metrics, Zariski topology, and schematic distance.

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16

Hrushovski, Ehud, and François Loeser. Non-Archimedean Tame Topology and Stably Dominated Types (AM-192). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.001.0001.

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Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed and model-theoretic prerequisites are reviewed in the first sections.

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17

Advances In Ultrametric Analysis 12th International Conference On Padic Functional Analysis July 26 2012 University Of Manitoba Winnipeg Canada. American Mathematical Society, 2013.

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18

Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices Ams Special Session Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices January 67 2012 Boston Ma. American Mathematical Society, 2013.

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