Between homeomorphism type and Tukey type

2019/02/16 by Milovich, David
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1902.06152

Abstract

Call a compact space X pin homogeneous if every two points a,b are pin equivalent, meaning that there exists a compact space Y, a quotient map f\colon Y→ X, and a homeomorphism g\colon Y→ Y such that gf^-1\a\=f^-1\b\. We will prove a representation theorem for pin equivalence; transitivity of pin equivalence will be a corollary. Pin homogeneity is strictly weaker than homogeneity and pin equivalence is strictly stronger than Tukey equivalence. Just as with topological homogeneity, no infinite compact F-space is pin homogeneous. On the other hand, X× 2^χ(X) is pin homogeneous for every compact X. And there is a compact pin homogeneous space with points of different π-character.

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