On The Relationships Between Types of L-convergence Spaces

This paper focuses on the relationships between stratified L-conver-gence spaces, stratified strong L-convergence spaces and stratifiedlevelwise  L-convergence spaces. It has been known that: (۱) astratified L-convergence space is precisely a left-continuousstratified levelwise L-convergence space; and (۲) a  stratifiedstrong 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  stratifiedlevelwise 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:

L-topology , Stratified L-filter , Stratified L-convergence space