typical contexts
Given a category of spaces equipped with a forgetful functor to Set thought of as producing for each space its underlying set of points, a codiscrete space (codiscrete object) on a set is, if it exists, the image under the right adjoint of .
Sometimes the codiscrete topology is also called the chaotic topology.
The dual concept is that of discrete space. For their relation see at discrete and codiscrete topology.
For the obvious forgetful functor from Top, a codiscrete space is a set with codiscrete topology.
A general axiomatization of the notion of space is as an object in a cohesive topos. This comes by definition with an underlying-set-functor (or similar) and a left adjoint that produces discrete cohesive structure. See there for details.
The terminology chaotic topology is motivated (see also at chaos) in
via footnote 3 in
and appears for instance in
Last revised on May 27, 2019 at 18:07:07. See the history of this page for a list of all contributions to it.