Antimatroids of finite character. (English) Zbl 0990.52001

Wahl, Nathalie

J. Geom. 70, No. 1-2, 168-175 (2001).

This paper provides an axiomatization of antimatroids (“convex geometries”; see P. H. Edelmann and R. E. Jamison, [Geom. Dedicata 19, 247-270 (1985; Zbl 0577.52001)]) that also works for the moderately infinite case of “finite character”, where any union of a chain of closed sets is again closed.

Reviewer: Günter M.Ziegler (Berlin)

MSC:

52A01	Axiomatic and generalized convexity
05B35	Combinatorial aspects of matroids and geometric lattices
06A15	Galois correspondences, closure operators (in relation to ordered sets)

Keywords:

antimatroid; infinite rank; abstract convex geometries; anti-exchange closures

Citations:

Zbl 0577.52001