Approach structures and measures of connectedness
David Holgate, Mark Sioen · Quaestiones Mathematicae · 2007
Measures of connectedness versus disconnectedness are introduced in anarbitrary topological construct as fixed points of a Galois connection. This places measures of connectedness found in the literature in a general categorical frame-work. An approach structure on a topological construct X is defined as a functorial assignment of approach distances to each object of X. Measures of separation and discreteness are then introduced and provide two factorisations of the above Galois connection through the collection of approach structures on X. This realizes connectedness and disconnectedness measures as approach notions and leads to suggestions for further investigation.