### 3-dimensional AR's which do not contain 2-dimensional ANR's

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that ${\left(\alpha \kappa \right)}^{\omega}$ is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage....

The body of this paper falls into two independent sections. The first deals with the existence of cross-sections in ${F}_{\sigma}$-decompositions. The second deals with the extensions of the results on accessibility in the plane.