Author/Authors :
Closure spaces have been previously investigated by Paul Edelman and Robert Jamison as ‘convex geometries’. Consequently، نويسنده , , a number of the results given here duplicate theirs. However، نويسنده , , we employ a slightly different، نويسنده , , but equivalent، نويسنده , , defining axiom which gives a new flavor to our presentation.
The major contribution is the definition of a partial order on all subsets، نويسنده , , not just closed (or convex) subsets. It is shown that the subsets of a closure space، نويسنده , , so ordered، نويسنده , , form a lattice with regular، نويسنده , , although non-modular، نويسنده , , properties. Investigation of this lattice becomes our primary focus.، نويسنده ,
