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Uniform continuity for all distance spaces

✍ Scribed by Paul Castillo; Gladys DiCristina; Darrell W. Hajek


Book ID
104295513
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
69 KB
Volume
98
Category
Article
ISSN
0166-8641

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✦ Synopsis


In this paper, we present a definition of uniform continuity which applies to morphisms in the category DST of distance spaces, and which generalizes the definitions of uniform continuity which apply in the categories of metric spaces, of nearness spaces and of zeroed distance spaces. This definition allows us to define a category BDUNIF, of d-bounded distance spaces and uniformly continuous functions (with this new definition of uniform continuity). TOP is embedded in BDUNIF as a bi-coreflective subcategory.


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