AbstractIn this paper, we introduce a new approach of proximity structure based on the grill notion. For G = P(X)nf g, we have the Efre- movi c proximity structure and for the other types of G , we have many types of proximity structures. Some results on these spaces have been obtained. Some of these results are : every G -normal T1space is G -proximizable space (Theorem 3.8). Also, for such space, we show that it has a unique com- patible G -proximity under the condition that X is compact relative to (Theorem 4.10). Finally, for a surjective map f : X ! (Y; f(G)) (G is a grill on X), we establish the largest G -proximity G on X for which the map f is a G -proximally continuous (Theorem 4.16).
|Keywords||G -proximity space, G -proximizable space, G -normal space, Grill.||Issue Date||29-Aug-2017||Publisher||Annals of Fuzzy Mathematics and Informatics||Journal||Annals of Fuzzy Mathematics and Informatics||URI||http://research.asu.edu.eg/handle/123456789/170166|
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