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Let $X$ be a regular first countable space of cellularity at most $2^\omega$. Is it true that the cardinality of $X$ is at most $2^\omega$? A cellular family is a family of pairwise disjoint non- …

Recall that a space $X$ is metaLindelof if every open cover of $X$ has a point-countable open refinement. A space $X$ is metacompact if every open cover of $X$ has a point-finite open refinem …

Is there a weakly Lindel\"of Tychonoff Moore non-ccc space? Note that here ccc denotes the countable chain condition; a space $X$ is called weakly Linde\"of if for any open cover $\mathcal U$ of $X$ …

As we know, every regular weakly Lindelof space is DCCC. Here DCCC denotes discrete countable chain condition, a space $X$ has discrete countable chain condition if every discrete family of non-empty …

A topological space has calibre $\aleph_1$ if for every uncountable sequence $\langle U_\alpha\mid\alpha\lt\aleph_1\rangle$ of nonempty open sets $U_\alpha\subset X$, there is an uncountable subfamily …

I am looking for a space as in the title, i.e., Is there a metacompact, normal, CCC space which is not Lindelof? A space is ccc iff any family of pairwise disjoint open sets is at most countable …

There is a statement as follows: If a Hausdorff (regular, Tychonoff) space $X$ has countable pseudocharacter and countable tightness, then the closure of any set $Y\subset X$ of cardinality $\le \ …