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Journal of Function Spaces
Volume 2017, Article ID 4901762, 7 pages
https://doi.org/10.1155/2017/4901762
Research Article

On Topological Properties of Metrics Defined via Generalized “Linking Construction”

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, 61-614 Poznań, Poland

Correspondence should be addressed to Marcin Borkowski; lp.ude.uma@krobm

Received 2 May 2017; Accepted 25 October 2017; Published 21 November 2017

Academic Editor: P. Veeramani

Copyright © 2017 Marcin Borkowski et al. 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 analyze topological properties of metric spaces obtained by using Száz’s construction, which we used to call generalized “linking construction.” In particular, we provide necessary and sufficient conditions for completeness of metric spaces obtained in this way. Moreover, we examine the relation between Száz’s construction and the “linking construction.” A particular attention is drawn to the “floor” metric, the analysis of which provides some interesting observations.