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On The Relationships Between Types of $L$-convergence Spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 13، شماره 1، اردیبهشت 2016، صفحه 93-103 اصل مقاله (324.7 K) | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2290 | ||
| نویسندگان | ||
Qiu Jin ؛ Lingqiang Li  ؛ Guangwu Meng
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| Department of Mathematics, Liaocheng University, Liaocheng, P.R.China | ||
| چکیده | ||
| This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratified levelwise $L$-convergence spaces. It has been known that: (1) a stratified $L$-convergence space is precisely a left-continuous stratified levelwise $L$-convergence space; and (2) a stratified strong $L$-convergence space is naturally a stratified $L$-convergence space, but the converse is not true generally. In this paper, a strong left-continuity condition for stratified levelwise $L$-convergence space is given. It is proved that a stratified strong $L$-convergence space is precisely a strongly left-continuous stratified levelwise $L$-convergence space. Then a sufficient and necessary condition for a stratified $L$-convergence space to be a stratified strong $L$-convergence space is presented. | ||
| کلیدواژه‌ها | ||
| $L$-topology؛ Stratified $L$-filter؛ Stratified $L$-convergence space | ||
| مراجع | ||
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