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A Reuniformization for Contractive Mappings in Uniform Spaces
Author(s) -
Angelov Vasil G.
Publication year - 1986
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19861270115
Subject(s) - mathematics , hausdorff space , space (punctuation) , pure mathematics , topology (electrical circuits) , discrete mathematics , combinatorics , philosophy , linguistics
Let X be a complete uniform HAUSDORFF space with a uniformity generated by a saturated family of pseudometrics = {ϱ α ( x , y ): α ϵ A } and let T : X → X be a continuous mapping. The paper contains necessary and sufficient conditions for the existence of a new family of pseudometrics *={ϱ α * *( x , y ): α*ϵ A *} generated the same topology such that T is contractive with respect to *.
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