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

Access to Document

10.1016/0166-8641(91)90061-P

Cite this

@article{0a1b8ab269d64e378af38ec02e69e255,

title = "Embeddings of finite-dimensional spaces into finite products of 1-dimensional spaces",

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).",

keywords = "Covering dimension, embedding (closed embedding), hedgehog of spininess τ, residual set",

author = "Wojciech Olszewski",

year = "1991",

month = jun,

day = "18",

doi = "10.1016/0166-8641(91)90061-P",

language = "English (US)",

volume = "40",

pages = "93--99",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Embeddings of finite-dimensional spaces into finite products of 1-dimensional spaces

AU - Olszewski, Wojciech

PY - 1991/6/18

Y1 - 1991/6/18

N2 - 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).

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

UR - http://www.scopus.com/inward/record.url?scp=44949270875&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44949270875&partnerID=8YFLogxK

U2 - 10.1016/0166-8641(91)90061-P

DO - 10.1016/0166-8641(91)90061-P

M3 - Article

AN - SCOPUS:44949270875

SN - 0166-8641

VL - 40

SP - 93

EP - 99

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this