## Abstract and Applied Analysis

### Generalized Metric Spaces Do Not Have the Compatible Topology

Tomonari Suzuki

#### Abstract

We study generalized metric spaces, which were introduced by Branciari (2000). 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 458098, 5 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606559

Digital Object Identifier
doi:10.1155/2014/458098

Mathematical Reviews number (MathSciNet)
MR3248859

Zentralblatt MATH identifier
07022418

#### Citation

Suzuki, Tomonari. Generalized Metric Spaces Do Not Have the Compatible Topology. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 458098, 5 pages. doi:10.1155/2014/458098. https://projecteuclid.org/euclid.aaa/1412606559

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