CONTINUOUS FUNCTIONS ON LG-SPACES

By an l-generalized topological space, briefly an lg- space, we mean the ordered pair (f;  ) in which f is a frame and  is a subframe of f. this notion has been first introduced by a.r. aliabad and a. sheykhmiri in [lg-topology, bull. iran. math. soc., 41 (1), (2015), 239-258]. in this article, we define continuous functions on lg-spaces and determine conditions under which the continuous image of a compact element of an lg-space is compact. moreover, we introduce the concept of connectedness for lg-spaces and determine conditions under which the continuous image of a connected element of an lg-space is connected. in fact, we show that lg-spaces are models for topological spaces as well as frames are models for topologies.