Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology
In this article we show that a contra second countable bitopological space is a $p_1$-Lindelof space, but the converse is not true in general. We provide suitable example with the help of concepts of nest and interlocking from LOTS. The relation between pairwise regular spaces and $p_1$-normal spac...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2018-02-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/34701 |
| _version_ | 1827766548346961920 |
|---|---|
| author | Santanu Acharjee Kyriakos Papadopoulos Binod Chandra Tripathy |
| author_facet | Santanu Acharjee Kyriakos Papadopoulos Binod Chandra Tripathy |
| author_sort | Santanu Acharjee |
| collection | DOAJ |
| description |
In this article we show that a contra second countable bitopological space is a $p_1$-Lindelof space, but the converse is not true in general. We provide suitable example with the help of concepts of nest and interlocking from LOTS. The relation between pairwise regular spaces and $p_1$-normal spaces is studied. At the end, we propose some open questions which may enrich various concepts related to Lindelofness in a bitopological space and other areas of mathematical ideas.
|
| first_indexed | 2024-03-11T11:43:37Z |
| format | Article |
| id | doaj.art-5d2ae307b76f48738df789c44f77d0f1 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:43:37Z |
| publishDate | 2018-02-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-5d2ae307b76f48738df789c44f77d0f12023-11-09T18:21:55ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882018-02-0138110.5269/bspm.v38i1.34701Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopologySantanu Acharjee0Kyriakos Papadopoulos1Binod Chandra Tripathy2Economics and Computational Rationality Group Department of MathematicsKuwait University Department of MathematicsTripura University Department of Mathematics In this article we show that a contra second countable bitopological space is a $p_1$-Lindelof space, but the converse is not true in general. We provide suitable example with the help of concepts of nest and interlocking from LOTS. The relation between pairwise regular spaces and $p_1$-normal spaces is studied. At the end, we propose some open questions which may enrich various concepts related to Lindelofness in a bitopological space and other areas of mathematical ideas. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/34701$p_1$-Lindelofnesscontra second countable spacenestinterlocking |
| spellingShingle | Santanu Acharjee Kyriakos Papadopoulos Binod Chandra Tripathy Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology Boletim da Sociedade Paranaense de Matemática $p_1$-Lindelofness contra second countable space nest interlocking |
| title | Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology |
| title_full | Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology |
| title_fullStr | Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology |
| title_full_unstemmed | Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology |
| title_short | Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology |
| title_sort | note on p 1 lindelof spaces which are not contra second countable spaces in bitopology |
| topic | $p_1$-Lindelofness contra second countable space nest interlocking |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/34701 |
| work_keys_str_mv | AT santanuacharjee noteonp1lindelofspaceswhicharenotcontrasecondcountablespacesinbitopology AT kyriakospapadopoulos noteonp1lindelofspaceswhicharenotcontrasecondcountablespacesinbitopology AT binodchandratripathy noteonp1lindelofspaceswhicharenotcontrasecondcountablespacesinbitopology |