query: proving closure of a subset
positive_passages.docid: 148824
positive_passages.text: Is associative binary operator closed on this subset?
negative_passages.docid: 126897
negative_passages.text: Showing the set $A+B$ is closed.
negative_passages.docid: 91991
negative_passages.text: How do I prove that two closed sets are separable?
negative_passages.docid: 66948
negative_passages.text: Proving question on sets
negative_passages.docid: 111032
negative_passages.text: Proof of Sets involving the Cartesian Product
negative_passages.docid: 41477
negative_passages.text: Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
negative_passages.docid: 124234
negative_passages.text: Prove that if $X$ and it's closure $\overline X$ are connected and if $X\subset Y \subset \overline X$, show that Y is also connected.
negative_passages.docid: 47056
negative_passages.text: Show that the boundary of a set equals the boundary of its complement
negative_passages.docid: 13906
negative_passages.text: How to prove the set $S$ is closed under the binary operation $a*b=a+b+kab$?
negative_passages.docid: 39708
negative_passages.text: Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
negative_passages.docid: 95244
negative_passages.text: Prove that a finite union of closed sets is also closed
negative_passages.docid: 154363
negative_passages.text: Prove that $\text{aff}(X) = \text{aff}(\text{closure}(X))$
negative_passages.docid: 147013
negative_passages.text: Subset of a finite set is finite
negative_passages.docid: 116009
negative_passages.text: Proving that if a set is both open and closed then it is equal to the real numbers
negative_passages.docid: 19856
negative_passages.text: Prove that a subset of a separable set is itself separable
negative_passages.docid: 43584
negative_passages.text: Separability and normal closure
negative_passages.docid: 13575
negative_passages.text: Need help for proving that: $f(f^{-1}(A)) ⊆ A$