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

2 votes
0 answers
56 views

Is a “well-behaved” closed subbasis for the topology generated by a closure operator a close...

Let $\Omega$ be a set, $\mathcal{c}: \mathcal{P}(\Omega) \rightarrow \mathcal{P}(\Omega)$ be a closure operator (i.e., $\mathcal{c}$ satisfies $X \subseteq \mathcal{c}(X)$ and $\mathcal{c}(\mathcal{c} …
David Gao's user avatar
  • 2,830
0 votes
0 answers
96 views

Does weak $L^2$ approximation implies $L^2$ approximation under a condition similar to conve...

(Cross posted from Math StackExchange: Does weak $L^2$ approximation implies $L^2$ approximation under a condition similar to convexity?) Assume $(\Omega, \mu)$ is a probability space. Consider a clas …
David Gao's user avatar
  • 2,830
3 votes
0 answers
15 views

Does there exist a multi-valued "monotone" and "compact" map from a Boolean algebra to the "...

This is a follow-up to my previous question, which has a negative answer. Here is the most general version that I'm interested: Does there exist a Boolean algebra $A$, an infinite cardinal $\kappa$, …
David Gao's user avatar
  • 2,830