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

Wojciech Olszewski

doi:10.1016/0166-8641(91)90061-P

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

Wojciech Olszewski^*

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	93-99
Number of pages	7
Journal	Topology and its Applications
Volume	40
Issue number	1
DOIs	https://doi.org/10.1016/0166-8641(91)90061-P
State	Published - 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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10.1016/0166-8641(91)90061-P

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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).",

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AB - 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).

KW - Covering dimension

KW - embedding (closed embedding)

KW - hedgehog of spininess τ

KW - residual set

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