Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

Near-embedding; singular set; Bing conjecture; recognition problem; space filling map; cellular decomposition; shrinkability

Hrčak ID:

36958

URI

https://hrcak.srce.hr/36958

Datum izdavanja:

21.5.2009.

Posjeta: 1.060 *