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Topology

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Moderate

Equations Relating Boundary, Closure, and Interior

TOPO-XL57YG

For a set $A$ in some topological space, denote by $bd(A)$, $cl(A)$, and $int(A)$ the boundary, closure, and interior of $A$, respectively. Which of the following identities relates the boundary, closure, and interior for any set $A$ in any topological space?

Select ALL that apply.

A

$bd(A) = cl(A) - int(A)$

B

$bd(A)\cap cl(A) = bd(A)$

C

$int(cl(A))=bd(A)$

D

$bd(A)\cup int(A)= cl(A)$

E

$bd(cl(A))=int(A)$