Geodesic
The Family of Lodato Proximities Compatible With a Given Topological Space
Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 388-404

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

Let (X, ) be a topological space. By we denote the family of all Lodato proximities on X which induce . We show that is a complete distributive lattice under set inclusion as ordering. Greatest lower bound and least upper bound are characterized. A number of techniques for constructing elements of are developed. By means of one of these constructions, all covers of any member of can be obtained. Several examples are given which relate to the lattice of all compatible proximities of Čech and the family of all compatible proximities of Efremovič. The paper concludes with a chart which summarizes many of the structural properties of , and . 
Thron, W. J.; Warren, R. H. The Family of Lodato Proximities Compatible With a Given Topological Space. Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 388-404. doi: 10.4153/CJM-1974-040-7
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