Some new results on six types mappings between $L$-convex spaces

Abstract

The aim of this paper is devoted to present some new results on six kinds of special mappings between $L$-convex spaces. For this purpose, we first make a summary about some novel elementary properties of $L$-CP mappings and $L$-CC mappings.
Secondly, we propose the definitions of almost $L$-CC mappings,
$L$-isomorphic mappings and $L$-embedding mappings and investigate their fundamental
characterizations. Finally, we establish the connections between $L$-quotient mappings and $L$-quotient spaces. As a summary, we give a diagram to show the relationships among all the above-mentioned mappings.