By an $l$-generalized topological space, briefly an $LG$-space, we mean the ordered pair $(F,\tau)$ in which $F$ is a frame and $\tau$ 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.
Rezai Aliabad, A., & Zarepour, H. (2021). CONTINUOUS FUNCTIONS ON LG-SPACES. Journal of Algebraic Systems, 8(2), 181-200. doi: 10.22044/jas.2020.9599.1471
MLA
A. Rezai Aliabad; H. Zarepour. "CONTINUOUS FUNCTIONS ON LG-SPACES". Journal of Algebraic Systems, 8, 2, 2021, 181-200. doi: 10.22044/jas.2020.9599.1471
HARVARD
Rezai Aliabad, A., Zarepour, H. (2021). 'CONTINUOUS FUNCTIONS ON LG-SPACES', Journal of Algebraic Systems, 8(2), pp. 181-200. doi: 10.22044/jas.2020.9599.1471
VANCOUVER
Rezai Aliabad, A., Zarepour, H. CONTINUOUS FUNCTIONS ON LG-SPACES. Journal of Algebraic Systems, 2021; 8(2): 181-200. doi: 10.22044/jas.2020.9599.1471
)
