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Invertibility, Often

Ethan Akin, Benjamin Weiss

Abstract

By using a similar pattern of arguments, we show that in three categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at measure preserving maps on Polish measure spaces. Finally, we examine continuous, measure preserving maps on Cantor spaces equipped with so-called good measures.

Invertibility, Often

Abstract

By using a similar pattern of arguments, we show that in three categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at measure preserving maps on Polish measure spaces. Finally, we examine continuous, measure preserving maps on Cantor spaces equipped with so-called good measures.

Paper Structure

This paper contains 4 sections, 24 equations.

Table of Contents

  1. Introduction
  2. Cantor Spaces
  3. Measure Spaces
  4. Good Measures on Cantor Spaces

Theorems & Definitions (16)

  • proof
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  • ...and 6 more