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New separation axioms on closure spaces generated by relations
RIA GUPTA,A.K. Das 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.1
It is evident from recent developments that topological structures which are more general than usual topology has many applications in allied branches of Science and Engineering. Cech closure space dened by Cech [3] being a generalized topo- logical space has been utilized in digital topology [4, 10, 11], a theory developed in late 1960s for the study of geometric and topological properties of digital im- ages [5, 6, 8, 9]. Cech closure spaces are obtained from the Kuratowski ones by omitting the conditions of idempotency. In 2006, Allam, Bakeir and Abo-Tabl [1] introduced a new approach to dene closure spaces through relations and stud- ied lower separation axioms, continuous functions and subspaces on closure spaces generated by relations. In 2008, the same authors [2] introduced some methods to generate topologies via binary relations. G. Liu [7] in 2010, utilized the notion of aftersets and foresets [1] which is renamed as R-left and R-right relative sets in [7]. In the present paper, we introduced and studied higher separation axioms on closure spaces generated by relations. Let X be any set then a relation on X is a subset of X x X, i.e., R⊆ X x X. The formula (x; y) ∈ R is abbreviated as xRy means that x is in relation R with y.
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Ria Gupta,Mrudula Joshi,Latika Gupta 대한의학회 2021 Journal of Korean medical science Vol.36 No.9
Video abstracts (VAs) are a motion picture equivalent of written abstracts. With greater use of social media platforms for post publication promotions of research articles, VAs have gained increasing popularity among researchers in recent years. Widespread lockdowns and social distancing protocols in the pandemic period furthered the use of VAs as a tool for efficient learning. Moreover, these may be the preferred medium for communicating certain types of information, such as diagnostic or therapeutic procedures, qualitative research, perspectives, and techniques. In this article, the authors discuss the role of VAs in the advancement of academic research, plausible designs, freeware for making videos, and specific considerations for crafting good VAs.
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