G -Proximity Spaces
A. Kandil; S. A. El-Sheikh; saed, Eman;
Abstract
In 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).
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).
Other data
| Title | G -Proximity Spaces | Authors | A. Kandil ; S. A. El-Sheikh ; saed, Eman | 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 |
Attached Files
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