Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/7758
Title: Separated and Connected Maps
Authors: Clementino, Maria Manuel 
Tholen, Walter 
Issue Date: 1998
Citation: Applied Categorical Structures. 6:3 (1998) 373-401
Abstract: Using on the one hand closure operators in the sense of Dikranjan and Giuli and on the other hand left- and right-constant subcategories in the sense of Herrlich, Preuß, Arhangel'skii and Wiegandt, we apply two categorical concepts of connectedness and separation/disconnectedness to comma categories in order to introduce these notions for morphisms of a category and to study their factorization behaviour. While at the object level in categories with enough points the first approach exceeds the second considerably, as far as generality is concerned, the two approaches become quite distinct at the morphism level. In fact, left- and right-constant subcategories lead to a straight generalization of Collins' concordant and dissonant maps in the category $$\mathcal{T}op$$ of topological spaces. By contrast, closure operators are neither able to describe these types of maps in $$\mathcal{T}op$$, nor the more classical monotone and light maps of Eilenberg and Whyburn, although they give all sorts of interesting and closely related types of maps. As a by-product we obtain a negative solution to the ten-year-old problem whether the Giuli–Hušek Diagonal Theorem holds true in every decent category, and exhibit a counter-example in the category of topological spaces over the 1-sphere.
URI: http://hdl.handle.net/10316/7758
DOI: 10.1023/A:1008636615842
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

Files in This Item:
File Description SizeFormat 
obra.pdf240.89 kBAdobe PDFView/Open
Show full item record

Page view(s) 50

203
checked on Jun 12, 2019

Download(s) 20

995
checked on Jun 12, 2019

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.