Topology in a Category: Compactness
Abstract: In a category with a subobject structure and a closure operator, we provide a categorical
theory of compactness and perfectness which yields a number of classical results of
general topology as special cases, including the product theorems by Tychonoff and
Frolik, the existence of Stone-Cech compactifications, both for spaces and maps,
and the Henriksen-Isbell characterization of perfect
maps of Tychonoff spaces.
Applications to other categories yield, among other things,
an alternative proof for the productivity of categorically
compact groups.
