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Abstract and Applied Analysis
Volume 2014, Article ID 458098, 5 pages
http://dx.doi.org/10.1155/2014/458098
Research Article

Generalized Metric Spaces Do Not Have the Compatible Topology

1Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Received 12 May 2014; Accepted 9 July 2014; Published 4 August 2014

Academic Editor: Wei-Shih Du

Copyright © 2014 Tomonari Suzuki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.