Abstract
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: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) 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.
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