Axiomatic systems of Alexandrov spaces
In order to study internel axiomatic systems and ordered features of Alexandrov spaces, with the help of some existed results in topology and locale theory, by restricting the related structures into Alexandrov setting, some equivalent descriptions are obtained. The results show that Alexandrov spac...
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Hebei University of Science and Technology
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doaj-2860c6b2ea8f4872a5cc14ad5146c47a2020-11-24T23:30:19ZzhoHebei University of Science and TechnologyJournal of Hebei University of Science and Technology1008-15422017-08-0138435235910.7535/hbkd.2017yx04006b201704006Axiomatic systems of Alexandrov spacesShanshan ZHANG0Fei LI1Wei YAO2School of Science, Hebei University of Science and Technology, Shijiazhuang,Hebei 050018, ChinaSchool of Science, Beijing Forest University, Beijing 100081, ChinaSchool of Science, Hebei University of Science and Technology, Shijiazhuang,Hebei 050018, ChinaIn order to study internel axiomatic systems and ordered features of Alexandrov spaces, with the help of some existed results in topology and locale theory, by restricting the related structures into Alexandrov setting, some equivalent descriptions are obtained. The results show that Alexandrov spaces are categorically isomorphic to Alexandrov neighborhood systems, Alexandrov closure operators, Alexandrov interior operators and Alexandrov derived operators; T0 Alexandrov spaces are isomorphic to posets and dual to complete-generated lattices. Alexandrov spaces can be completely characterized by neighborhood systems, closure operators, interior operators, derived system, the specialization order and the point-free order.http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201704006&flag=1&journal_topologyAlexandrov spaceneighborhood systemclosure operatorinterior operatorderivation operatorspecialization ordercomplete-generated lattice |
collection |
DOAJ |
language |
zho |
format |
Article |
sources |
DOAJ |
author |
Shanshan ZHANG Fei LI Wei YAO |
spellingShingle |
Shanshan ZHANG Fei LI Wei YAO Axiomatic systems of Alexandrov spaces Journal of Hebei University of Science and Technology topology Alexandrov space neighborhood system closure operator interior operator derivation operator specialization order complete-generated lattice |
author_facet |
Shanshan ZHANG Fei LI Wei YAO |
author_sort |
Shanshan ZHANG |
title |
Axiomatic systems of Alexandrov spaces |
title_short |
Axiomatic systems of Alexandrov spaces |
title_full |
Axiomatic systems of Alexandrov spaces |
title_fullStr |
Axiomatic systems of Alexandrov spaces |
title_full_unstemmed |
Axiomatic systems of Alexandrov spaces |
title_sort |
axiomatic systems of alexandrov spaces |
publisher |
Hebei University of Science and Technology |
series |
Journal of Hebei University of Science and Technology |
issn |
1008-1542 |
publishDate |
2017-08-01 |
description |
In order to study internel axiomatic systems and ordered features of Alexandrov spaces, with the help of some existed results in topology and locale theory, by restricting the related structures into Alexandrov setting, some equivalent descriptions are obtained. The results show that Alexandrov spaces are categorically isomorphic to Alexandrov neighborhood systems, Alexandrov closure operators, Alexandrov interior operators and Alexandrov derived operators; T0 Alexandrov spaces are isomorphic to posets and dual to complete-generated lattices. Alexandrov spaces can be completely characterized by neighborhood systems, closure operators, interior operators, derived system, the specialization order and the point-free order. |
topic |
topology Alexandrov space neighborhood system closure operator interior operator derivation operator specialization order complete-generated lattice |
url |
http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201704006&flag=1&journal_ |
work_keys_str_mv |
AT shanshanzhang axiomaticsystemsofalexandrovspaces AT feili axiomaticsystemsofalexandrovspaces AT weiyao axiomaticsystemsofalexandrovspaces |
_version_ |
1725541839253012480 |