On The Relationships Between Types of $L$-convergence Spaces

Authors

Department of Mathematics, Liaocheng University, Liaocheng, P.R.China

Abstract

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.

Keywords


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