ON THE S_{\lambda}(X) AND {\lambda}-ZERO DIMENSIONAL SPACES | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 1، آذر 2022، صفحه 179-188 اصل مقاله (158.22 K) | ||
| نوع مقاله: Research Note | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.10906.1535 | ||
| نویسندگان | ||
| S. Soltanpour* 1؛ S. Mehran2 | ||
| 1Department of Science, Petroleum University of Technology, P.O. Box 6318714317, Ahvaz, Iran. | ||
| 2Department of Science, Ahvaz Islamic Azad University, P.O. Box 6134937333, Ahvaz, Iran. | ||
| چکیده | ||
| Let $S_\lambda(X)=\{f\in C(X) : |X\setminus Z(f)|<\lambda\}$, such that $\lambda$ is a regular cardinal number with $\lambda\leq |X|$. It is generalization of $C_F (X)=S_{\aleph_0}(X)$ and $SC_F(X)=S_{\aleph_1}(X)$. Using this concept we extend some of the basic results concerning the socle to $S_\lambda(X)$. It is shown that if $X$ is a $\lambda$-pseudo discrete space, then $C_{K,\lambda}(X)\subseteq S_{\lambda}(X)$. $S_{\lambda}$-completely regular spaces are investigated. Consequently, $X$ is a $S_{\aleph_1}$-completely regular space if and only if $X$ is $\aleph_1$-zero dimensional space. $S_{\lambda}P$-spaces are introduced and studied. | ||
| کلیدواژهها | ||
| $lambda$-super socle of $C(X)$؛ $lambda$-zero dimensional space؛ $S_{lambda}$-completely regular space؛ $S_{lambda}P$- space | ||
| مراجع | ||
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