Soft C-continuity and soft almost C-continuity between soft topological spaces

Abstract

We present the notions of soft c-continuity and soft nearly c-continuity, which are weaker versions of soft continuity and soft almost continuity, respectively. We obtain several characterizations for these two concepts. We show that soft c-continuity and soft almost c-continuity are preserved under soft restrictions. In addition, we investigate the conditions under which the composition of two soft c-continuous and soft almost c-continuous functions is soft c-continuous and soft almost c-continuous. Moreover, via soft $N$-open sets, we give a characterization of the soft compactness of soft topological spaces over finite sets of parameters. In addition, we show that for a given soft topological space $(L,\Omega ,F)$, the collection of soft regular open sets with soft compact complements forms a soft base for some coarser soft topology. We demonstrate that $(L,{\Omega }^{⁎},F)$ are all soft compacts. Furthermore, we demonstrate that $\Omega ={\Omega }^{⁎}$ if $(L,\Omega ,F)$ or $(L,{\Omega }^{⁎},F)$ is soft compact and soft Hausdorff. Finally, we investigate the correspondences between the novel notions in soft topology and their general topological analogs.

Keywords: Almost c-continuous functions; Almost continuous functions; Soft Hausdorff; Soft almost continuous functions; Soft compact; Soft continuous functions; c-continuous functions.