Abstract
Let K be a CW-complex. A map f : X → Y of compacta X and Y is said to be of e-dim ≤ K if e-dim f-1 (y) ≤ K for every y ε Y. We prove that if e-dim f ≤ K then there exists a σ-compact subset A of X such that e-dim A ≤ K and f|x\A is 0-dimensional. This result is an analogue for extensional dimension of a well-known theorem of Torunczyk.
Original language | English |
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Pages (from-to) | 33-35 |
Number of pages | 3 |
Journal | Topology and its Applications |
Volume | 103 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2000 |
Externally published | Yes |
Keywords
- 0-dimensional maps
- Compacta
- Extensional dimension
ASJC Scopus subject areas
- Geometry and Topology