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Homotopy lifting property in symmetric products

Eduardo Blanco-Gómez

Abstract

In this paper we prove the homotopy lifting property for symmetric products $SP_{m}(X)$ and $F_{m}(X)$, with $X$ a Hausdorff topological space. Furthermore, we introduce a new tool, the theory of topological puzzles, to get a useful decomposition of $X^{m}$.

Homotopy lifting property in symmetric products

Abstract

In this paper we prove the homotopy lifting property for symmetric products and , with a Hausdorff topological space. Furthermore, we introduce a new tool, the theory of topological puzzles, to get a useful decomposition of .

Paper Structure

This paper contains 6 sections, 27 theorems, 154 equations.

Table of Contents

  1. Introduction
  2. Symmetric products $SP_{m}(X)$ and $F_{m}(X)$
  3. Exterior and interior boundaries of a set
  4. Passings-through
  5. Homotopy lifting property in $SP_{m}(X)$
  6. Homotopy lifting property in $F_{m}(X)$

Key Result

Lemma 3.6

Let $X$ be a topological space and $A\subset X$. Then,

Theorems & Definitions (91)

  • Remark 3.1
  • Remark 3.2
  • Definition 3.3
  • Remark 3.4
  • Remark 3.5
  • Lemma 3.6
  • proof
  • proof
  • Lemma 3.8
  • proof
  • ...and 81 more