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

Repovš, D.; Rosicki, W.; Zastrow, A.; Željko, M.

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

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Description

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}.