A metrizable semitopological semilattice with non-closed partial order
We construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-04-01
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| Series: | Topological Algebra and its Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/taa-2020-0006 |
| _version_ | 1831725300759658496 |
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| author | Banakh Taras Bardyla Serhii Ravsky Alex |
| author_facet | Banakh Taras Bardyla Serhii Ravsky Alex |
| author_sort | Banakh Taras |
| collection | DOAJ |
| description | We construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice, having a prescribed countable family of convergent sequences. |
| first_indexed | 2024-12-21T04:37:22Z |
| format | Article |
| id | doaj.art-a9725cbee10e417c81cf34c860fc5406 |
| institution | Directory Open Access Journal |
| issn | 2299-3231 |
| language | English |
| last_indexed | 2024-12-21T04:37:22Z |
| publishDate | 2020-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Topological Algebra and its Applications |
| spelling | doaj.art-a9725cbee10e417c81cf34c860fc54062022-12-21T19:15:49ZengDe GruyterTopological Algebra and its Applications2299-32312020-04-0181677510.1515/taa-2020-0006taa-2020-0006A metrizable semitopological semilattice with non-closed partial orderBanakh Taras0Bardyla Serhii1Ravsky Alex2Ivan Franko National University of Lviv (Ukraine) and Jan Kochanowski University in Kielce,PolandInstitute of Mathematics, Kurt Gödel Research Center, Vienna, AustriaDepartment of Analysis, Geometry and Topology, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of UkraineWe construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice, having a prescribed countable family of convergent sequences.https://doi.org/10.1515/taa-2020-0006semitopological semilatticepartial orderconvergent sequenceactsemigroup54a2006a1222a2637b05 |
| spellingShingle | Banakh Taras Bardyla Serhii Ravsky Alex A metrizable semitopological semilattice with non-closed partial order Topological Algebra and its Applications semitopological semilattice partial order convergent sequence act semigroup 54a20 06a12 22a26 37b05 |
| title | A metrizable semitopological semilattice with non-closed partial order |
| title_full | A metrizable semitopological semilattice with non-closed partial order |
| title_fullStr | A metrizable semitopological semilattice with non-closed partial order |
| title_full_unstemmed | A metrizable semitopological semilattice with non-closed partial order |
| title_short | A metrizable semitopological semilattice with non-closed partial order |
| title_sort | metrizable semitopological semilattice with non closed partial order |
| topic | semitopological semilattice partial order convergent sequence act semigroup 54a20 06a12 22a26 37b05 |
| url | https://doi.org/10.1515/taa-2020-0006 |
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