pith. sign in

arxiv: math/0507062 · v1 · pith:CHDGOPE5new · submitted 2005-07-04 · 🧮 math.GN · math.FA

Small Valdivia compact spaces

classification 🧮 math.GN math.FA
keywords valdiviaclasscompactcompactaretractionsunderweightaleph
0
0 comments X
read the original abstract

We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\loe\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.