TY - JOUR AU - Al-Shami, T. M. AU - Ameen, Z. A. AU - Abu-Gdairi, R. AU - Mhemdi, A. PY - 2023 TI - Continuity and separation axioms via infra-topological spaces JO - Journal of Mathematics and Computer Science SP - 213--225 VL - 30 IS - 3 AB - 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 infra-topological 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 infra-quotient 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, \(i=0,1,\ldots, 4\)). 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. SN - ISSN 2008-949X UR - https://doi.org/10.22436/jmcs.030.03.03 DO - 10.22436/jmcs.030.03.03 ID - Al-Shami2023 ER -