On Soft Submaximal and Soft Door Spaces (Contemporary Mathematics, 2025)
This paper is divided into two parts. The first part deals with soft submaximal spaces, where we present new theorems and some basic facts. Further, we successfully find a requirement that indicates the soft one-point compactification of a soft topological space is soft submaximal. In the second part, we study soft door spaces. We notice that every soft door space is a soft submaximal space, but a soft submaximal space need not be soft door. The class of soft door spaces is hereditary. We give couterexamples showing that this class is neither additive nor productive. We further show that images of soft door spaces under certain soft functions are also soft door spaces. After that, we characterize certain soft topological spaces in terms of soft limit points and the Krull dimension. At last, we discuss when the soft one-point compactification of a soft topological space is soft door.
Keywords: soft one-point compactification space; soft door space; soft submaximal space; krull dimension of soft topological space