Mappings and universality.
type: Item
instance of: scholarly article
title: Mappings and universality.
zbMATH Open document ID: 1048.54008
DOI: 10.1016/S0166-8641(03)00207-4
author: S. D. Iliadis
published in: Topology and its Applications
publication date: 2004-03-14T00:00:00Z
review text: The author considers classes consisting of mappings, whose domains and ranges are spaces of weight less than or equal to a given infinite cardinal denoted by \(\tau\). The notion of a saturated class of mappings is given and the following results are proved: (a) in each saturated class of mappings there exist universal elements, (b) the intersection of not more than \(\tau\) many saturated classes of mappings is also a saturated class, (c) the class of the domains and the class of the ranges of all elements of a saturated class of mappings are saturated classes of spaces, and (d) the (non-empty) class of all mappings (respectively, of all open mappings), whose domains belong to a given saturated class of spaces and ranges belong to another saturated class of spaces, is saturated.
Mathematics Subject Classification ID: 54B99
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 2056851
zbMATH Keywords: universal space
zbMATH Keywords: universal mapping
zbMATH Keywords: saturated class of spaces
zbMATH Keywords: saturated class of mappings
reviewed by: Shou Lin
MaRDI profile type: Publication
cites work: Q4855460
cites work: A construction of containing spaces
cites work: On the countable sum of zero-dimensional metric spaces
cites work: Countable Dimensional Universal Sets
cites work: A universal separable metric locally finite-dimensional space
description: scientific article; zbMATH DE number 2056851