Locally compact connected T1 with more than one point implies resolvable

Statement
A topological space with more than one point that is locally compact, connected, and T1, must be a resolvable space.

Applications

 * Manifold is either discrete or resolvable
 * Continuum with more than one point is resolvable

Facts used

 * 1) uses::Connected and T1 with at least two points implies no isolated points
 * 2) uses::Locally compact without isolated points implies resolvable

Proof
The proof follows directly from Facts (1) and (2).