The Family of Lodato Proximities Compatible With a Given Topological Space
- 1 April 1974
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 26 (2) , 388-404
- https://doi.org/10.4153/cjm-1974-040-7
Abstract
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 .Keywords
This publication has 3 references indexed in Scilit:
- On topologically induced generalized proximity relations. IIPacific Journal of Mathematics, 1966
- On topologically induced generalized proximity relationsProceedings of the American Mathematical Society, 1964
- Indexed Systems of Neighborhoods for General Topological SpacesThe American Mathematical Monthly, 1961