University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401$L$-Topological Spaces1191332838710.22130/scma.2017.28387ENAli BajravaniDepartment of Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran.Journal Article20170212By 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.http://scma.maragheh.ac.ir/article_28387_de42aeb44cc0345bcda542f42caad0ac.pdf