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Santi Spadaro
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A space with independent tightness

Recall that the tightness of a topological space $X$ is defined as the least cardinal $\kappa$ such that for every non-closed subset $A$ of $X$ and every point $x \in \overline{A} \setminus A$, there is a set $B \subset A$ such that $|B| \leq \kappa$ and $x \in \overline{B}$.

QUESTION: Is there a ZFC example of a space whose tightness cannot be determined in ZFC?

Santi Spadaro
  • 4.4k
  • 31
  • 40