Embeddings of finite-dimensional spaces into finite products of 1-dimensional spaces

Wojciech Olszewski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In the present paper, for an arbitrary infinite cardinal number τ, we construct a 1-dimensional completely metrizable absolute retract M of weight τ such that for every n-dimensional metrizable (completely metrizable) space X of weight not greater than τ, the set of all embeddings (closed embeddings) of X into Mn+1 is residual in the function space C(X,Mn+1).

Original languageEnglish (US)
Pages (from-to)93-99
Number of pages7
JournalTopology and its Applications
Volume40
Issue number1
DOIs
StatePublished - Jun 18 1991

Keywords

  • Covering dimension
  • embedding (closed embedding)
  • hedgehog of spininess τ
  • residual set

ASJC Scopus subject areas

  • Geometry and Topology

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