# 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
- Disciplines

## 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.

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