Approximate maps, filter monad, and a representation of localic maps

Bernhard Banaschewski and Aleš Pultr

Department of Mathematics and Statistics, McMaster University, 1280 Main St. W, Hamilton, Ontario L8S 4K1, Canada
Department of Applied Mathematics and ITI, MFF, Charles University, CZ 11800 Praha 1, Malostranské nám. 25


Abstract: A covariant representation of the category of locales by approximate maps (mimicking a natural representation of continuous maps between spaces in which one approximates points by small open sets) is constructed. It is shown that it can be given a Kleisli shape, as a part of a more general Kleisli representation of meet preserving maps. Also, we present the spectrum adjunction in this approximation setting.

AMSclassification: primary 06D22; secondary 18C20.

Keywords: frames (locales), localic maps, approximation, Kleisli representation.