Item Details

Transformations of Antimatroid Closure Spaces

Pfaltz, John; Karro, John
Format
Report
Author
Pfaltz, John
Karro, John
Abstract
Investigation of the transformations of vector spaces, whose most abstract formulations are called matroids, is basic in mathematics; but transformations of discrete spaces have received relatively little attention. This paper develops the concept of transformations of discrete spaces in the context of antimatroid closure spaces. The nature of these transformations are quite different from those encountered in linear algebra because the underlying spaces are strikingly different. The transformation properties of “closed”, “continuous” and “order preserving” are defined and explored. The classic graph transformations, homomorphism and topological sort, are examined in the context of these properties. Then we define a deletion which we believe plays a central role in discrete transformations. Antimatroid closure spaces, when partially ordered, can be interpreted as lattices. We show that deletions induce lower semihomomorphisms between the corresponding lattices.
Language
English
Date Received
20121029
Published
University of Virginia, Department of Computer Science, 1998
Published Date
1998
Collection
Libra Open Repository
Logo for In CopyrightIn Copyright

Availability

Access Online