Extension properties of Stone–Čech coronas and proper absolute extensors
Volume 222 / 2013
Abstract
We characterize, in terms of $X$, the extensional dimension of the Stone–Čech corona $\beta X \setminus X$ of a locally compact and Lindelöf space $X$. The non-Lindelöf case is also settled in terms of extending proper maps with values in $I^{\tau }\setminus L$, where $L$ is a finite complex. Further, for a finite complex $L$, an uncountable cardinal $\tau $ and a $Z_{\tau }$-set $X$ in the Tikhonov cube $I^{\tau }$ we find a necessary and sufficient condition, in terms of $I^{\tau }\setminus X$, for $X$ to be in the class $\operatorname {AE}([L])$. We also introduce a concept of a proper absolute extensor and characterize the product $[0,1)\times I^{\tau }$ as the only locally compact and Lindelöf proper absolute extensor of weight $\tau > \omega $ which has the same pseudocharacter at each point.
