Time:  12:00  13:20 
Room: 
Doherty Hall 4303

Speaker: 
Peter Nyikos Department of Mathematics University of South Carolina 
Title: 
Topological applications of large cardinal numbers

Abstract:  Some axioms of set theory related to large cardinal numbers, and their effects on topology, will be discussed. Some very useful combinatorial axioms require us to assume the consistency of very large cardinals; others are so durable that it requires the consistency of very large cardinals to negate them. One pair of recent contrasting theorems involves the following problem: if a compact Hausdorff space has a dense subspace of cardinality strictly less than the space itself, must it have an uncountable subspace with a countable dense subspace? 