Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43793
Title: More on Subfitness and Fitness
Authors: Picado, Jorge 
Pultr, Aleš 
Issue Date: 2014
Publisher: Springer
Project: PEst-C/MAT/UI0324/2011 
Serial title, monograph or event: Applied Categorical Structures
Volume: 23
Issue: 3
Abstract: The concepts of fitness and subfitness (as defined in Isbell, Trans. Amer. Math. Soc. 327, 353–371, 1991) are useful separation properties in point-free topology. The categorical behaviour of subfitness is bad and fitness is the closest modification that behaves well. The separation power of the two, however, differs very substantially and subfitness is transparent and turns out to be useful in its own right. Sort of supplementing the article (Simmons, Appl. Categ. Struct. 14, 1–34, 2006) we present several facts on these concepts and their relation. First the “supportive” role subfitness plays when added to other properties is emphasized. In particular we prove that the numerous Dowker-Strauss type Hausdorff axioms become one for subfit frames. The aspects of fitness as a hereditary subfitness are analyzed, and a simple proof of coreflectivity of fitness is presented. Further, another property, prefitness, is shown to also produce fitness by heredity, in this case in a way usable for classical spaces, which results in a transparent characteristics of fit spaces. Finally, the properties are proved to be independent.
URI: http://hdl.handle.net/10316/43793
Other Identifiers: 10.1007/s10485-014-9366-7
DOI: 10.1007/s10485-014-9366-7
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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