Affordable Access

Publisher Website

Universal finite-to-one map and universal countable dimensional spaces

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
68
Issue
2
Identifiers
DOI: 10.1016/0166-8641(95)00050-x
Keywords
  • Countable Dimensional Space
  • Universal Space
  • Finite-To-One Map
  • Universal Map
  • Ar-Map
  • Absorber
Disciplines
  • Mathematics

Abstract

Abstract There is a closed finite-to-one map t́f of a zero-dimensional, separable, metric absolute G δσ -set X onto a space Y such that for any closed, finite-to-one map f′: X′ → Y′ of separable, metric spaces, with dim X′ ⩽ 0, there exist embeddings i : X′ → X and j : Y′ → Y such that fi = jf. In particular, the space Y is universal for all separable metric spaces which are countable dimensional. We also show that finite-to-one maps produce naturally cell-like maps. Finally, using the method of absorbers we prove a topological characterization of the space σ × N>, where σ is Smirnov's universal strongly countable dimensional space and N is Nagata's universal countable dimensional space.

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

On countable-to-one maps

on Topology and its Applications Jan 01, 2007

A few remarks concerning countable unions of finit...

on Topology and its Applications Jan 01, 1995

Finite-to-one maps

on Topology and its Applications Jan 01, 2008
More articles like this..