Sequential Completeness for ⊤-Quasi-Uniform Spaces and a Fixed Point Theorem

Gunther Jäger
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Gunther Jäger: School of Mechanical Engineering, University of Applied Sciences Stralsund, 18435 Stralsund, Germany

Mathematics, 2022, vol. 10, issue 13, 1-22

Abstract: We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. We show that completeness implies sequential completeness and that for ⊤-uniform spaces with countable ⊤-uniform bases, completeness and sequential completeness are equivalent. As an illustration of the applicability of the concept, we give a fixed point theorem for certain contractive self-mappings in a ⊤-uniform space. This result yields, as a special case, a fixed point theorem for probabilistic metric spaces.

Keywords: ?-sequence; ?-quasi-uniform space; completeness; sequential completeness; fixed point theorem; probabilistic metric space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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