CONTINUOUS FUNCTIONS ON LG-SPACES

By an l-generalized topological space, briefly an LG-space, we mean the ordered pair (F,τ) in which F is a frame and τ 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.