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Sequence-covering maps on submetrizable spaces

Vlad Smolin

Abstract

A topological space is called a submetrizable if it can be mapped onto a metrizable topological space by a continuous one-to-one map. In this paper we answer two questions concerning sequence-covering maps on submetrizable spaces.

Sequence-covering maps on submetrizable spaces

Abstract

A topological space is called a submetrizable if it can be mapped onto a metrizable topological space by a continuous one-to-one map. In this paper we answer two questions concerning sequence-covering maps on submetrizable spaces.
Paper Structure (3 sections, 4 theorems, 22 equations)

This paper contains 3 sections, 4 theorems, 22 equations.

Table of Contents

  1. Introduction
  2. Notation and terminology
  3. A theorem and an example

Key Result

Lemma 4

There exists a decomposition $\{A_i\ \colon\ i\in\omega\}$ of $\omega$ such that $A_i < A_j$ whenever $i < j$. ∎

Theorems & Definitions (7)

  • Lemma 4
  • Lemma 5
  • proof
  • Theorem 6
  • proof
  • Theorem 7
  • proof