Generalized quotient topologies and hereditary classes

Montagantirud, Pongdate; Phonrakkhet, S.

doi:10.1007/s10474-020-01039-0

Cited by 1 publication

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Minimal structure [30], weak structure [21], generalized weak structure [18], ordered structure [8] and so on are examples of these types of structures. Many researchers have also examined these concepts in depth; see, [19,22,33]. In fact, over the last two decades, the entire research field has developed.…”

Section: Introductionmentioning

confidence: 99%

Continuity and separation axioms via infra-topological spaces

Al-Shami¹,

Ameen²,

Abu-Gdairi³

et al. 2022

J. Math. Computer Sci.

View full text Add to dashboard Cite

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.

show abstract