Property C and closed maps
type: Item
instance of: scholarly article
title: Property C and closed maps
zbMATH Open document ID: 0608.54006
DOI: 10.1016/0166-8641(87)90063-0
author: Dennis J. Garity
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: A standard theorem from dimension theory states that a closed \((m+1)\) to 1 map defined on a finite dimensional space can raise dimension by at most m. Dimension raising maps on countable dimensional spaces and on weakly infinite dimensional spaces have been investigated by A. V. Arkhangelskij, A. I. Vajnshtejn and E. G. Sklyarenko. A typical theorem is that a closed map on such spaces raises dimension only if some point has an uncountable number of preimages. A class of infinite dimensional spaces closely related to the two types mentioned above is the class of C spaces. R. Pol's example in 1980 and recent work of F. D. Ancel have generated renewed interest in C spaces. The author proves results about dimension raising maps on C spaces analogous to the results mentioned above.
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 3984091
zbMATH Keywords: weakly infinite dimensional spaces
zbMATH Keywords: countable dimensional spaces
zbMATH Keywords: C spaces
zbMATH Keywords: dimension raising maps
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90063-0
OpenAlex ID: W2054574958
cites work: A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandrof's problem
cites work: The Role of Countable Dimensionality in the Theory of Cell-Like Relations
cites work: Closed mappings, bicompact sets and a problem of P. S. Aleksandrov
cites work: Q4185470
cites work: Q4775149
cites work: A near-selection theorem
cites work: A class of infinite-dimensional spaces. Part II: An Extension Theorem and the theory of retracts
cites work: A Weakly Infinite-Dimensional Compactum which is not Countable-Dimensional
cites work: New dimension-theory techniques for constructing infinite-dimensional examples
cites work: Q3264659
cites work: Q5729716
description: scientific article; zbMATH DE number 3984091