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

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

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...

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Main Authors: Marcin Borkowski, Dariusz Bugajewski, Adam Burchardt
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2017/4901762
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spelling doaj-2a095c12ed534dd480ad7972882705c22020-11-25T01:00:37ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/49017624901762On Topological Properties of Metrics Defined via Generalized “Linking Construction”Marcin Borkowski0Dariusz Bugajewski1Adam Burchardt2Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, 61-614 Poznań, PolandFaculty of Mathematics and Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, 61-614 Poznań, PolandFaculty of Mathematics and Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, 61-614 Poznań, PolandWe 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.http://dx.doi.org/10.1155/2017/4901762
collection DOAJ
language English
format Article
sources DOAJ
author Marcin Borkowski
Dariusz Bugajewski
Adam Burchardt
spellingShingle Marcin Borkowski
Dariusz Bugajewski
Adam Burchardt
On Topological Properties of Metrics Defined via Generalized “Linking Construction”
Journal of Function Spaces
author_facet Marcin Borkowski
Dariusz Bugajewski
Adam Burchardt
author_sort Marcin Borkowski
title On Topological Properties of Metrics Defined via Generalized “Linking Construction”
title_short On Topological Properties of Metrics Defined via Generalized “Linking Construction”
title_full On Topological Properties of Metrics Defined via Generalized “Linking Construction”
title_fullStr On Topological Properties of Metrics Defined via Generalized “Linking Construction”
title_full_unstemmed On Topological Properties of Metrics Defined via Generalized “Linking Construction”
title_sort on topological properties of metrics defined via generalized “linking construction”
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2017-01-01
description 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.
url http://dx.doi.org/10.1155/2017/4901762
work_keys_str_mv AT marcinborkowski ontopologicalpropertiesofmetricsdefinedviageneralizedlinkingconstruction
AT dariuszbugajewski ontopologicalpropertiesofmetricsdefinedviageneralizedlinkingconstruction
AT adamburchardt ontopologicalpropertiesofmetricsdefinedviageneralizedlinkingconstruction
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