On relatively connected sublocales and J-frames | ||
| Categories and General Algebraic Structures with Applications | ||
| دوره 22، شماره 1، فروردین 2025، صفحه 181-196 اصل مقاله (500.53 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.2024.235270.1481 | ||
| نویسندگان | ||
| Simo S. Mthethwa* ؛ Siyabonga Dubazana | ||
| School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa. | ||
| چکیده | ||
| In this paper, we present a study of relatively connected sublocales. Connected sublocales are relatively connected, not conversely. We study conditions under which relatively connected sublocales are connected. The development of this study is subsequently utilized to characterize what we call C-normal frames. We show that normal frames are C-normal but not conversely. Some results concerning J-frames are presented; amongst other things, we prove that regular continuous frames are rim-compact. A rim-compact J-frame is regular continuous. The latter is used to show that the least compactification of a regular continuous J-frame coincides with its Freudenthal compactification. In turn, this contributes to the known conditions under which the least compactification is perfect. | ||
| کلیدواژهها | ||
| J-frames؛ relatively connected sublocales؛ C-normal؛ Freudenthal؛ continuous frames؛ perfect compactification؛ rim-compact | ||
| مراجع | ||
|
[1] Baboolal, D., Perfect compactifications of frames, Czech. Math. J. 61 (2011), 845-861. [2] Baboolal, D., Conditions under which the least compactification of a regular continuous frame is perfect, Czech. Math. J. 62(137) (2012), 505-515. [3] Banaschewski, B., “Lectures on Frames”, University of Cape Town, Cape Town, 1987. [4] Banaschewski, B., Compactification of frames, Math. Nachr. 149 (1990), 105-115. [5] Ferreira, M.J., Picado, J., and Pinto, S.M., Remainders in pointfree topology, Topology Appl. 245 (2018), 21-45. [6] Isbell, J.R., First steps in descriptive theory of locales, Trans. Amer. Math. Soc. 327 (1991), 353-371; Corrections. 341 (1994), 467-468. [7] Johnstone, P.T., “Stone Spaces”, Cambridge University Press, 1982. [8] Michael, E., J-spaces, Topology Appl. 102 (2000), 315-339. [9] Mthethwa, S.S., Perfectness of 2-star compactifications of frames, Topology Appl. 297 (2021), 107701. [10] Mthethwa, S.S., Characterising certain compactifications of frames with special attention to Freudenthal, Algebra Univers. 82 (2021), article number 14. [11] Mthethwa, S.S., On J-frames, Topology Appl. 342 (2024), 108772. [12] Mthethwa, S.S. and Taherifar, A., J-spaces and C-normal Spaces: An Algebraic Perspective, Filomat. 38 (2024), 1009-1021. [13] Mthethwa, S.S. and Taherifar, A., A note on J-spaces and relatively connected subsets, Quaest. Math. 46 (2023), 2453- 2464. [14] Picado, J. and Pultr, A., “Frames and Locales: Topology without Points”, Frontiers in Mathematics, Springer, Basel, 2012. [15] Plewe, T., Quotient maps of locales, Appl. Categ. Structures 8 (2000), 17-44. | ||
|
آمار تعداد مشاهده مقاله: 255 تعداد دریافت فایل اصل مقاله: 531 |
||