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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

1 vote
1 answer
118 views

Trivial convergent sequences in $\beta X$

Let $X$ be a Tychonoff space and denote by $\beta X$ its Stone-Čech compactification. We know, for example, that if $X$ is an $F$-space then $\beta X$ is an $F$-space and, therefore, in $\beta X$, the …
Carlos Jiménez's user avatar
4 votes
0 answers
116 views

When $X$ is homeomorphic to $\mathscr{F}[X]$?

While I was talking to some colleagues, one of them said that there exists a topological space $X$ such that $X$ is uncountable, non-discrete and homeomorphic to $\mathscr{F}[X]$ (the Pixley-Roy hyper …
Carlos Jiménez's user avatar