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Fuzzy uniform convergence and equicontinuity

✍ Scribed by Gunther Jäger

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
125 KB
Volume
109
Category
Article
ISSN
0165-0114

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✦ Synopsis

In our earlier papers we investigated function space structures in FTS, the category of fuzzy topological spaces and in FCS, the category of fuzzy convergence spaces. This paper is devoted to the study of function space structures in FUS, the category of fuzzy uniform spaces due to Lowen. We develop the basic theory and give examples of such structures such as pointwise and compact convergence. We consider separation axioms in these fuzzy function spaces and show that the fuzzy uniformity of uniform convergence is conjoining for C(X; Y ). We deÿne a notion of equicontinuous sets of mappings on which pointwise and compact convergence coincide.

📜 SIMILAR VOLUMES

Equicontinuity, uniform continuity and s
Equicontinuity, uniform continuity and sequences in topological groups
✍ Jean Pierre Troallic 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 146 KB

Let G be an almost metrizable topological group (for example, a locally compact group). This paper is concerned with the proof of two principal results. First, the following criterion for equicontinuity is proved: Let X be a union of G δ -subsets of G, Y a uniform space and H a set of continuous map