Papers by Jeremiah Lee Morgan
Topology and its Applications, 2015
Let P be a directed set and X a space. A collection C of subsets of X is P-locally finite if C = ... more Let P be a directed set and X a space. A collection C of subsets of X is P-locally finite if C = {Cp : p ∈ P } where (i) if p ≤ p ′ then Cp ⊆ C p ′ and (ii) each Cp is locally finite. Then X is P-paracompact if every open cover has a P-locally finite open refinement. Further, X is P-metrizable if it has a (P × N)-locally finite base. This work provides the first detailed study of P-paracompact and P-metrizable spaces, particularly in the case when P is a K(M), the set of all compact subsets of a separable metrizable space M ordered by set inclusion.
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Papers by Jeremiah Lee Morgan