Glasnik matematički, Vol. 44 No. 1, 2009.
Original scientific paper
https://doi.org/10.3336/gm.44.1.16
Constructing near-embeddings of codimension one manifolds with countable dense singular sets
D. Repovš
orcid.org/0000-0002-6643-1271
; Institute of Mathematics, Physics and Mechanics and Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
W. Rosicki
; Institute of Mathematics, Gdansk University, Gdansk, Poland
A. Zastrow
; Institute of Mathematics, Gdansk University, Gdansk, Poland
M. Željko
; Institute of Mathematics, Physics and Mechanics and Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
Abstract
We present, for all n ≥ 3, very simple examples of continuous maps f : Mn-1 → Mn from closed (n-1)-manifolds Mn-1 into closed n-manifolds Mn such that even though the singular set S(f) of f is countable and dense, the map f can nevertheless be approximated by an embedding, i.e. f is a near-embedding. In dimension 3 one can get even a piecewise-linear approximation by an embedding.
Keywords
Near-embedding; singular set; Bing conjecture; recognition problem; space filling map; cellular decomposition; shrinkability
Hrčak ID:
36958
URI
Publication date:
21.5.2009.
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