It is commonly known that some topological spaces include structures that may be used to expand abstract notions. Primal structure is one such sort of structure. We provided the primal Hausdorff class of spaces, which included the class of all Hausdorff spaces. Furthermore, we provide the concepts of primal regular spaces and primal normal spaces. We present new theorems and results.
Citation: Ahmad Al-Omari, Ohud Alghamdi. Regularity and normality on primal spaces[J]. AIMS Mathematics, 2024, 9(3): 7662-7672. doi: 10.3934/math.2024372
It is commonly known that some topological spaces include structures that may be used to expand abstract notions. Primal structure is one such sort of structure. We provided the primal Hausdorff class of spaces, which included the class of all Hausdorff spaces. Furthermore, we provide the concepts of primal regular spaces and primal normal spaces. We present new theorems and results.
| [1] |
D. Jankovic, T. R. Hamlett, New topologies from old via ideals, Am. Math. Mon., 97 (1990), 295–310. https://doi.org/10.2307/2324512 doi: 10.2307/2324512
|
| [2] | K. Kuratowski, Topologie: Volume I, London: Academic Press, 1966. |
| [3] |
G. Choquet, Sur les notions de filter et grille, C. R. Math. Acad. Sci. Paris, 224 (1947), 171–173. https://doi.org/10.2307/2324512 doi: 10.2307/2324512
|
| [4] | R. Vaidyanathaswamy, Set topology, Chelsea Publishing Company, 1960. |
| [5] |
T. R. Hamlett, D. Rose, $*$-topological properties, Int. J. Math. Math. Sci., 13 (1990), 507–512. https://doi.org/10.1155/S0161171290000734 doi: 10.1155/S0161171290000734
|
| [6] |
A. Al-Omari, T. Noiri, On $\Psi_{\mathcal{G}}$-sets in grill topological spaces, Filomat, 25 (2011), 187–196. https://doi.org/10.2298/FIL1102187A doi: 10.2298/FIL1102187A
|
| [7] | B. Roy, M. N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math., 33 (2007), 771–786. |
| [8] |
S. Modak, Topology on grill-filter space and continuity, Bol. Soc. Parana. Mat., 13 (2013), 219–230. https://doi.org/10.5269/bspm.v31i2.16603 doi: 10.5269/bspm.v31i2.16603
|
| [9] |
H. Al-Saadi, H. Al-Malki, Generalized primal topological spaces. AIMS Math., 8 (2023), 24162–24175. https://doi.org/10.3934/math.20231232 doi: 10.3934/math.20231232
|
| [10] | S. Acharjee, M. Özkoç, F. Y. Issaka, Primal topological spaces, arXiv Preprint, 2022. |
| [11] |
A. Al-Omari, S. Acharjee, M. Özkoç, A new operator of primal topological spaces, Mathematica, 65 (2023), 175–183. https://doi.org/10.24193/mathcluj.2023.2.03 doi: 10.24193/mathcluj.2023.2.03
|
| [12] |
A. Al-Omari, M. H. Alqahtani, Primal structure with closure operators and their applications, Mathematics, 11 (2023), 4946. https://doi.org/10.3390/math11244946 doi: 10.3390/math11244946
|
| [13] |
B. C. Tripathy, M. Sen, S. Nath, On generalized difference ideal convergence in generalized probabilistic $n$-normed spaces, P. Natl. A. Sci. India A, 91 (2021), 29–34. https://doi.org/10.1007/s40010-019-00644-1 doi: 10.1007/s40010-019-00644-1
|
| [14] |
H. Albayrak, Ö. Ölmez, S. Aytar, Some set theoretic operators preserving ideal Hausdorff convergence, Real Anal. Exch., 47 (2022), 179–190. https://doi.org/10.14321/realanalexch.47.1.1618849755 doi: 10.14321/realanalexch.47.1.1618849755
|
| [15] |
T. M. Al-shami, Z. A. Ameen, R. Abu-Gdairi, A. Mhemdi, On primal soft topology, Mathematics, 11 (2023), 2329. https://doi.org/10.3390/math11102329 doi: 10.3390/math11102329
|
| [16] | C. J. Isham, An introduction to general topology and quantum topology, In: Physics, Geometry and Topology, Boston: Springer, 1990,129–189. https://link.springer.com/chapter/10.1007/978-1-4615-3802-8_5 |
Ahmad Al-Omari, Ohud Alghamdi. Regularity and normality on primal spaces[J]. AIMS Mathematics, 2024, 9(3): 7662-7672. doi: 10.3934/math.2024372
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