CONTINUOUS FUNCTIONS ON LG-SPACES | ||
| Journal of Algebraic Systems | ||
| دوره 8، شماره 2، فروردین 2021، صفحه 181-200 اصل مقاله (208.69 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2020.9599.1471 | ||
| نویسندگان | ||
| A. Rezai Aliabad* ؛ H. Zarepour | ||
| Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. | ||
| چکیده | ||
| By an $l$-generalized topological space, briefly an $LG$-space, we mean the ordered pair $(F,\tau)$ in which $F$ is a frame and $\tau$ is a subframe of $F$. This notion has been first introduced by A.R. Aliabad and A. Sheykhmiri in [$LG$-topology, { Bull. Iran. Math. Soc}., 41 (1), (2015), 239-258]. In this article, we define continuous functions on $LG$-spaces and determine conditions under which the continuous image of a compact element of an $LG$-space is compact. Moreover, we introduce the concept of connectedness for $LG$-spaces and determine conditions under which the continuous image of a connected element of an $LG$-space is connected. In fact, we show that $LG$-spaces are models for topological spaces as well as frames are models for topologies. | ||
| کلیدواژهها | ||
| frame؛ LG-space؛ compact element؛ adjoint mapping؛ continuous mapping | ||
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آمار تعداد مشاهده مقاله: 485 تعداد دریافت فایل اصل مقاله: 556 |
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