Some generalizations of Fedorchuk duality theorem—I

Some Generalizations of Fedorchuk Duality Theorem – I

Generalizing Duality Theorem of V. V. Fedorchuk [11], we prove Stone-type duality theorems for the following four categories: all of them have as objects the locally compact Hausdorff spaces, and their morphisms are, respectively, the continuous skeletal maps, the quasi-open perfect maps, the open maps, the open perfect maps. In particular, a Stone-type duality theorem for the category of all c...

Some Generalizations of Fedorchuk Duality Theorem – II Georgi

This paper is a continuation of the paper [4]. In [4] it was shown that there exists a duality Ψa between the category DSkeLC (introduced there) and the category SkeLC of locally compact Hausdorff spaces and continuous skeletal maps. We describe here the subcategories of the category DSkeLC which are dually equivalent to the following eight categories: all of them have as objects the locally co...

A Duality in Integral Geometry; Some Generalizations of the Radon

Generalizations of Matroid Duality

Matroid duality is an important generalization of duality for planar graphs. Using unpublished notes of Brylawski, we extend this notion to arbitrary set systems. This allows one to define a generalized Tutte polynomial. We examine this polynomial for several set systems that are not matroids, and we also investigate the combinatorial significance of duality for these set systems.

Map Duality and Generalizations

A map is an embedding of a graph into a surface so that each face is simply connected. Geometric duality, whereby vertices and faces are reversed, is a classic construction for maps. A generalization of map duality is given and discussed both graph and group theoretically.