‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.

a. csaszar introduced and extensively studied the notionof generalized open sets. following csazar, we introduce a new notionsuperconnected. the main purpose of this paper is to study generalizedsuperconnected spaces. various characterizations of generalized super-connected spaces and preservation theorems are discussed.