2 problems

Let $X$ be a locally compact, non-compact, separable metrizable space, and let $X^*$ denote its Stone–Čech remainder. An autohomeomorphism of $X^*$ is a homeomorphism from $X^*$ to…

Let $X$ and $Y$ be locally compact Polish spaces. For a locally compact space $X$, write $X^* = \beta X\setminus X$ for its Stone–Čech remainder, and call a homeomorphism between s…