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New basic result in classical descriptive set theory: Preservation of completeness

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
156
Issue
9
Identifiers
DOI: 10.1016/j.topol.2009.03.001
Keywords
  • Borel Space
  • Completely Metrizable Space
  • Open Map
  • Closed Map
  • S-Covering Map
  • Stable Map

Abstract

Abstract The aim of this note is to prove the following result: Assume that f is a continuous function from the space of irrationals ω ω onto Y such that the image f ( U ) of every set U which is open and closed in ω ω is the union of one open and one closed set. Then Y is a completely metrizable space.

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