Constructing near-embeddings of codimension one manifolds with countable dense singular sets

Details Constructing near-embeddings of codimension one manifolds with countable dense singular sets Constructing near-embeddings of codimension one manifolds with countable dense singular sets

2008-03-29

arxiv.org/abs/0803.4251v1

Glasnik Mat. 44 (64):1 (2009), 255-258.

Mathematics

Geometric Topology

Scientific paper

The purpose of this paper is to present, for all $n\ge 3$, very simple
examples of continuous maps $f:M^{n-1} \to M^{n}$ from closed $(n-1)$-manifolds
$M^{n-1}$ into closed $n$-manifold $M^n$ 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 {\sl near-embedding}.

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