On the dimension of growth of mappings
type: Item
instance of: scholarly article
title: On the dimension of growth of mappings
zbMATH Open document ID: 0553.54011
author: V. P. Norin
published in: Moscow University Mathematics Bulletin
publication date: 1982-01-01T00:00:00Z
review text: In ibid. 1982, No.4, 33-36 (1982; Zbl 0508.54023) the author described m- proximities for a \(T_ 1\) space X with a given map \(f: X\to Y\) and their induced bicompactifications \(\delta_ fX\) and \(f_{\delta}\). Here he uses m-proximities to define a covering type of dimension for X and f and proves them equal, respectively to the usual covering dimension of the remainder \(N=\delta_ fX\setminus X\) and of \(f_{\delta}| N\). This extends to mappings some results of \textit{Yu. M. Smirnov} [Mat. Sb., Nov. Ser. 69(111), 141-160 (1966; Zbl 0161.424)].
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54E05
zbMATH DE Number: 3881463
zbMATH Keywords: m-proximities
zbMATH Keywords: bicompactifications
zbMATH Keywords: covering dimension
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3881463