A NOTE ON Cc(X) VIA A TOPOLOGICAL RING | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 2، فروردین 2023، صفحه 323-334 اصل مقاله (157.41 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11467.1579 | ||
| نویسندگان | ||
| R. Mohamadian1؛ M. Namdari* 1؛ H. Najafian1؛ S. Soltanpour2 | ||
| 1Department of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box 6135783151, Ahvaz, Iran. | ||
| 2Department of Science, Petroleum University of Technology, P.O. Box 6318714317, Ahvaz, Iran. | ||
| چکیده | ||
| Let $C_c(X)$ (resp., $C_c^*(X)$) denote the functionally countable subalgebra of $C(X)$ (resp., $C^*(X)$), consisting of all functions (resp., bounded functions) with countable image. $C_c(X)$ (resp., $C_c^*(X)$) as a topological ring via $m_c$-topology (resp., $m^*_c$-topology) and $u_c$-topology (resp., $u^*_c$-topology) is investigated and the equality of the latter two topologies is characterized. Topological spaces which are called $N$-spaces are introduced and studied. It is shown that the $m_c$-topology on $C_c(X)$ and its relative topology as a subspace of $C(X)$ (with $m$-topology) coincide if and only if $X$ is an $N$-space. We also show that $X$ is pseudocompact if and only if it is both a countably pseudocompact, and an $N$-space. | ||
| کلیدواژهها | ||
| functionally countable subalgebra؛ $m_c$-topology؛ $u_c$-topology؛ $N$-space | ||
| مراجع | ||
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