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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2407.13334 |
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| _version_ | 1866929426308005888 |
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| author | Nxumalo, Mbekezeli |
| author_facet | Nxumalo, Mbekezeli |
| contents | We define and characterize the notion of (i,j)-Baireness for bilocales. We also give internal properties of (i,j)-Baire bilocales which are not translated from properties of (i,j)-Baireness in bispaces. It turns out (i,j)-Baire bilocales are conservative in bilocales, in the sense that a bitopological space is almost (i,j)-Baire if and only if the bilocale it induces is (i,j)-Baire. Furthermore, in the class of Noetherian bilocales, (i,j)-Baireness of a bilocale coincides with (i,j)-Baireness of its ideal bilocale. We also consider relative versions of (i,j)-Baire where we show that a bilocale is (i,j)-Baire only if the subbilocale induced by the Booleanization is (i,j)-Baire. We use the characterization of (i,j)-Baire bilocales to introduce and characterize (τ_{i},τ_{j})-Baireness in the category of topobilocales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13334 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the category of (i,j)-Baire Bilocales Nxumalo, Mbekezeli General Topology 06D22 We define and characterize the notion of (i,j)-Baireness for bilocales. We also give internal properties of (i,j)-Baire bilocales which are not translated from properties of (i,j)-Baireness in bispaces. It turns out (i,j)-Baire bilocales are conservative in bilocales, in the sense that a bitopological space is almost (i,j)-Baire if and only if the bilocale it induces is (i,j)-Baire. Furthermore, in the class of Noetherian bilocales, (i,j)-Baireness of a bilocale coincides with (i,j)-Baireness of its ideal bilocale. We also consider relative versions of (i,j)-Baire where we show that a bilocale is (i,j)-Baire only if the subbilocale induced by the Booleanization is (i,j)-Baire. We use the characterization of (i,j)-Baire bilocales to introduce and characterize (τ_{i},τ_{j})-Baireness in the category of topobilocales. |
| title | On the category of (i,j)-Baire Bilocales |
| topic | General Topology 06D22 |
| url | https://arxiv.org/abs/2407.13334 |