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Generalized metric spaces do not have the compatible topology. (English) Zbl 1470.54017

Summary: We study generalized metric spaces, which were introduced by A. Branciari [Publ. Math. 57, No. 1–2, 31–37 (2000; Zbl 0963.54031)]. In particular, generalized metric spaces do not necessarily have the compatible topology. Also we prove a generalization of the Banach contraction principle in complete generalized metric spaces.

MSC:

54E35 Metric spaces, metrizability
54E50 Complete metric spaces

Citations:

Zbl 0963.54031
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Full Text: DOI

References:

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