In this article, we start with some properties of several types of soft continuous and soft open functions. We primarily focus on studying soft continuous (soft open) and soft irresolute (soft anti-irresolute) functions. We show that soft continuous and soft irresolute functions are independent and correspondingly soft open and soft anti-irresolute functions. On the other hand, soft bi-continuity implies soft bi-irresoluteness but not the other way round. Moreover, we find conditions under which soft bi-irresoluteness and soft bi-continuity are similar.

In this paper, we first explore more properties of soft somewhere dense continuous functions. Then, we discuss the preservation of soft Baire property and soft Baire category. We give some concrete examples to illustrate how our findings extend some conclusions and connections made in the literature.

In order to investigate a particular topic in mathematics, more specifically, general topology, it is always desirable to find a weaker condition. This work is planned to study a weak (topological) structure named infra-topological space. An infratopological space is the collection of subsets of a universe that includes the empty set and is closed under finite intersections. The continuity, openness, and homeomorphism of mappings between infra-topological spaces are explored. Through the use of some examples, analogous properties and characterizations of ordinary mappings cannot be hopped on infra-topological structures. Then, the concepts of product and coproduct of infra-topological spaces are analyzed. Furthermore, the notion of infra-quotient topologies, which are inspired by infra-continuity, is introduced. The essential properties indicate that infraquotient topologies and ordinary quotient topologies act in parallel. The final part of this paper is devoted to the investigation of infra separation axioms (infra T i -spaces, i = 0, 1, . . . , 4). The behaviour of ordinary separation axioms cannot be translated to an infra-topological structure. More precisely, infra-T 3 and infra-T 4 -spaces are independent, and singletons need not be infra-closed in infra-T 1 -spaces.