On Metric-Type Spaces Based on Extended <i>T</i>-Conorms

Kirk and Shahzad introduced the class of strong b-metric spaces lying between the class of b-metric spaces and the class of metric spaces. As compared with b-metric spaces, strong b-metric spaces have the advantage that open balls are open in the induced topology and, hence, they have many propertie...

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Main Authors:	Tarkan Öner, Alexander Šostak
Format:	Article
Language:	English
Published:	MDPI AG 2020-07-01
Series:	Mathematics
Subjects:	metric b-metric sb-metric extended t-conorm ⊕-metric ⊕-b-metric
Online Access:	https://www.mdpi.com/2227-7390/8/7/1097

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spelling	doaj-d4656826ffc547b4b31c1bfe128009b62020-11-25T03:13:10ZengMDPI AGMathematics2227-73902020-07-0181097109710.3390/math8071097On Metric-Type Spaces Based on Extended <i>T</i>-ConormsTarkan Öner0Alexander Šostak1Department of Mathematics, Muğla Sıtkı Koçman University, Muğla 48000, TurkeyInstitute of Mathematics and CS and Department of Mathematics, University of Latvia, LV-1586 Riga, LatviaKirk and Shahzad introduced the class of strong b-metric spaces lying between the class of b-metric spaces and the class of metric spaces. As compared with b-metric spaces, strong b-metric spaces have the advantage that open balls are open in the induced topology and, hence, they have many properties that are similar to the properties of classic metric spaces. Having noticed the advantages of strong b-metric spaces Kirk and Shahzad complained about the absence of non-trivial examples of such spaces. It is the main aim of this paper to construct a series of strong b-metric spaces that fail to be metric. Realizing this programme, we found it reasonable to consider these metric-type spaces in the context when the ordinary sum operation is replaced by operation ⊕, where ⊕ is an extended t-conorm satisfying certain conditions.https://www.mdpi.com/2227-7390/8/7/1097metricb-metricsb-metricextended t-conorm⊕-metric⊕-b-metric
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tarkan Öner Alexander Šostak
spellingShingle	Tarkan Öner Alexander Šostak On Metric-Type Spaces Based on Extended <i>T</i>-Conorms Mathematics metric b-metric sb-metric extended t-conorm ⊕-metric ⊕-b-metric
author_facet	Tarkan Öner Alexander Šostak
author_sort	Tarkan Öner
title	On Metric-Type Spaces Based on Extended <i>T</i>-Conorms
title_short	On Metric-Type Spaces Based on Extended <i>T</i>-Conorms
title_full	On Metric-Type Spaces Based on Extended <i>T</i>-Conorms
title_fullStr	On Metric-Type Spaces Based on Extended <i>T</i>-Conorms
title_full_unstemmed	On Metric-Type Spaces Based on Extended <i>T</i>-Conorms
title_sort	on metric-type spaces based on extended <i>t</i>-conorms
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-07-01
description	Kirk and Shahzad introduced the class of strong b-metric spaces lying between the class of b-metric spaces and the class of metric spaces. As compared with b-metric spaces, strong b-metric spaces have the advantage that open balls are open in the induced topology and, hence, they have many properties that are similar to the properties of classic metric spaces. Having noticed the advantages of strong b-metric spaces Kirk and Shahzad complained about the absence of non-trivial examples of such spaces. It is the main aim of this paper to construct a series of strong b-metric spaces that fail to be metric. Realizing this programme, we found it reasonable to consider these metric-type spaces in the context when the ordinary sum operation is replaced by operation ⊕, where ⊕ is an extended t-conorm satisfying certain conditions.
topic	metric b-metric sb-metric extended t-conorm ⊕-metric ⊕-b-metric
url	https://www.mdpi.com/2227-7390/8/7/1097
work_keys_str_mv	AT tarkanoner onmetrictypespacesbasedonextendediticonorms AT alexandersostak onmetrictypespacesbasedonextendediticonorms
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On Metric-Type Spaces Based on Extended <i>T</i>-Conorms

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