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Let $A,B$ be subsets of space $X$.

I know that $\text{Cl}(A\cap B)\subseteq \text{Cl}(A)\cap \text{Cl}(B)$, but under which condition does $\text{Cl}(A)\cap \text{Cl}(B)\subseteq \text{Cl}(A\cap B)$?

Thanks

Sumanta
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tulepes
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1 Answers1

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This question has been answered here. For this condition to happen, we need a discrete topology.

Sam
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    It's not clear whether the OP is asking for conditions on the soace $X$, or conditions on the sets $A$ and $B$. – bof Oct 14 '22 at 10:47