On the hereditary paracompactness of locally compact, hereditarily normal spaces

TL;DR

This paper explores the conditions under which certain locally compact, hereditarily normal spaces are hereditarily paracompact, linking set-theoretic assumptions like supercompact cardinals to topological properties.

Contribution

It proves that assuming the consistency of a supercompact cardinal, all locally compact, hereditarily normal spaces without a perfect pre-image of omega_1 are hereditarily paracompact.

Findings

Establishes a set-theoretic consistency result for paracompactness in specific topological spaces.

Connects large cardinal assumptions to properties of topological spaces.

Provides conditions under which certain normal spaces are hereditarily paracompact.

Abstract

We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of omega_1 is hereditarily paracompact.