Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Universal Coverings for Limit and Pseudotopological Spaces

Jonathan Treviño-Marroquín

Abstract

Limit and Pseudotopological spaces are two generalizations of topological spaces which are defined by indicating what filters converge under some axioms. In this article, we introduce covering spaces and set forth some necessary conditions for a construction for a universal covering space.

Universal Coverings for Limit and Pseudotopological Spaces

Abstract

Limit and Pseudotopological spaces are two generalizations of topological spaces which are defined by indicating what filters converge under some axioms. In this article, we introduce covering spaces and set forth some necessary conditions for a construction for a universal covering space.
Paper Structure (15 sections, 50 theorems, 22 equations)

This paper contains 15 sections, 50 theorems, 22 equations.

Table of Contents

  1. Introduction
  2. Limit Spaces
  3. Basic notions and examples
  4. New spaces generated by old ones
  5. Homotopy
  6. Covering Spaces and Fibrations
  7. Covering Spaces
  8. Fibrations
  9. Lifting Theorem
  10. Universal Covering Space
  11. Definition and properties
  12. Construction
  13. pseudotopological Modification
  14. Basic notions on pseudotopological Spaces
  15. Covering Spaces on pseudotopological Spaces

Key Result

Lemma 2.1.3

Let $X$ be a limit space. $\mathcal{F}\rightarrow x$ if and only if $\mathcal{F}\cap [x] \rightarrow x$.

Theorems & Definitions (128)

  • Definition 2.1.1: Limit Space; Beattie_Butzmann_2002, 1.1.1
  • Definition 2.1.2: Beattie_Butzmann_2002, 1.1.3
  • Example 2.1.2.1
  • Example 2.1.2.2
  • Lemma 2.1.3
  • proof
  • Definition 2.1.4: Local Covering System; Beattie_Butzmann_2002, 1.3.28
  • Definition 2.2.1: Topological constructs; Preuss_2002, 1.1.1 and 1.1.2
  • Theorem 2.2.2: Existence of final structuresPreuss_2002, 1.2.1.1
  • Theorem 2.2.3: Preuss_2002, 2.2.12 and 2.3.1.5
  • ...and 118 more