Geodesic
On Large Inductive Dimension of Proximity Spaces
Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 961-973

Voir la notice de l'article provenant de la source Cambridge University Press

The notion of proximity spaces was introduced by Efremovic in [2, 3]. An analysis of proximity spaces was carried out by Smirnov in [5].The study of covering dimension of proximity spaces was originated by Smirnov in [6].In this paper we introduce the concept of δ-large inductive dimension of proximity spaces and study some of its properties. 1. Definitions and basic concepts. Definition 1. [5]A proximity space or (δ-space) is a pair (X, δ) where X is a set and δ is a mapping from 2X × 2X into the set {0, 1} satisfying the following axioms: 1. δ(A, B) = δ(B, A)∀ A, B ∊ 2 X. 2. δ(A, B ∪ C) = δ(A, B) δ(A, C) ∀ A, B, C ∊ 2X 3. δ({x}, {y}) = 0 ⇔ x = y. 4. δ(X, ∅) = 1. 5. δ(A, B) = 1 ⇒ ∃ C, D ∊ 2 X ∋ C ∪ D = X and δ(A, C) · δ(B, C) = 1. 
Kandil, A. On Large Inductive Dimension of Proximity Spaces. Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 961-973. doi: 10.4153/CJM-1983-052-7
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