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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 3 > No. 3


Generalized I-Proximity Spaces

PP: 173-178
A. Kandil, O. A. Tantawy, S. A. El-Sheikh, A. Zakaria,
An ideal on a set X is a nonempty collection of subsets of X with heredity property which is also closed finite unions. The purpose of this paper is to construct a new approach of generalized proximity based on the ideal notion. For I = {f }, we have the generalized proximity structure [15] and for the other types of I, we have many types of generalized proximity structures. In addition, if (X,t ) is an IR2−topological space, then t ∗ is a compatible with an I-Pervin proximity relation on P(X). It is also shown that if (X,t ) is a ∗−normal space and (X,t ∗) is a Ro−space, then t ∗ is a compatible with an I-Lodato proximity relation on P(X).

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