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Locally compact perfectly normal spaces may all be paracompact

Paul B. Larson;  Franklin D. Tall — 2010

Fundamenta Mathematicae

We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...

Universal functions

Paul B. Larson;  Arnold W. Miller;  Juris Steprāns;  William A. R. Weiss — 2014

Fundamenta Mathematicae

A function of two variables F(x,y) is universal if for every function G(x,y) there exist functions h(x) and k(y) such that G(x,y) = F(h(x),k(y)) for all x,y. Sierpiński showed that assuming the Continuum Hypothesis there exists a Borel function F(x,y) which is universal. Assuming Martin's Axiom there is a universal function of Baire class 2. A universal function cannot be of Baire class 1. Here we show that it is consistent that for each α with 2 ≤ α < ω₁ there...

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