Some topological aspects of interval spaces
In previous papers, several $ T_{0} $, $ T_{2} $ objects, $ D $-connectedness and zero-dimensionality in topological categories have been introduced and compared. In this paper, we characterize separated objects, $ T_{0} $, $ {\bf{T_{0}}} $, $ T_{1} $, Pre-$ T_{2} $ and several versions of Hausdorff...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023190?viewType=HTML |
| _version_ | 1797953914188857344 |
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| author | Muhammad Qasim Arbaz Jehan Khan Samirah Alsulami Shoaib Assar |
| author_facet | Muhammad Qasim Arbaz Jehan Khan Samirah Alsulami Shoaib Assar |
| author_sort | Muhammad Qasim |
| collection | DOAJ |
| description | In previous papers, several $ T_{0} $, $ T_{2} $ objects, $ D $-connectedness and zero-dimensionality in topological categories have been introduced and compared. In this paper, we characterize separated objects, $ T_{0} $, $ {\bf{T_{0}}} $, $ T_{1} $, Pre-$ T_{2} $ and several versions of Hausdorff objects in the category of interval spaces and interval-preserving mappings and examine their mutual relationship. Further, we give the characterization of the notion of closedness and $ D $-connectedness in interval spaces and study some of their properties. Finally, we introduce zero-dimensionality in this category and show its relation to $ D $-connectedness. |
| first_indexed | 2024-04-10T23:09:31Z |
| format | Article |
| id | doaj.art-ea2339faa6054abfa4e81a6c4e1a7cad |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T23:09:31Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ea2339faa6054abfa4e81a6c4e1a7cad2023-01-13T06:37:35ZengAIMS PressAIMS Mathematics2473-69882023-01-01823826384110.3934/math.2023190Some topological aspects of interval spacesMuhammad Qasim 0Arbaz Jehan Khan1Samirah Alsulami2Shoaib Assar31. Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), H-12 Islamabad, Pakistan1. Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), H-12 Islamabad, Pakistan2. Department of Mathematics, College of Science, University of Jeddah, Jeddah 21577, Saudi Arabia1. Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), H-12 Islamabad, PakistanIn previous papers, several $ T_{0} $, $ T_{2} $ objects, $ D $-connectedness and zero-dimensionality in topological categories have been introduced and compared. In this paper, we characterize separated objects, $ T_{0} $, $ {\bf{T_{0}}} $, $ T_{1} $, Pre-$ T_{2} $ and several versions of Hausdorff objects in the category of interval spaces and interval-preserving mappings and examine their mutual relationship. Further, we give the characterization of the notion of closedness and $ D $-connectedness in interval spaces and study some of their properties. Finally, we introduce zero-dimensionality in this category and show its relation to $ D $-connectedness.https://www.aimspress.com/article/doi/10.3934/math.2023190?viewType=HTMLinterval spaceconvex spaceseparatedhausdorffzero-dimensionalinitial lifttopological category |
| spellingShingle | Muhammad Qasim Arbaz Jehan Khan Samirah Alsulami Shoaib Assar Some topological aspects of interval spaces AIMS Mathematics interval space convex space separated hausdorff zero-dimensional initial lift topological category |
| title | Some topological aspects of interval spaces |
| title_full | Some topological aspects of interval spaces |
| title_fullStr | Some topological aspects of interval spaces |
| title_full_unstemmed | Some topological aspects of interval spaces |
| title_short | Some topological aspects of interval spaces |
| title_sort | some topological aspects of interval spaces |
| topic | interval space convex space separated hausdorff zero-dimensional initial lift topological category |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023190?viewType=HTML |
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