مشخصات پژوهش

‎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, ‎quotient and compactness notions‎, ‎where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and‎ ‎$L$-connected topological spaces‎, ‎respectively‎.