query: How do I prove that the product of two closed sets is closed?
positive_passages.docid: 143457
positive_passages.text: Is product of two closed sets closed?
negative_passages.docid: 140103
negative_passages.text: If product of two sets $A\times B$ is closed, are $A$ and $B$ closed?
negative_passages.docid: 78300
negative_passages.text: Showing a set is closed other than giving a counterexample?
negative_passages.docid: 15480
negative_passages.text: Open set in a metric space is union of closed sets
negative_passages.docid: 141762
negative_passages.text: The direct sum of two closed subspace is closed? (Hilbert space)
negative_passages.docid: 153934
negative_passages.text: How to prove that a set R\Z is open
negative_passages.docid: 143105
negative_passages.text: Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
negative_passages.docid: 148992
negative_passages.text: A finite set is closed
negative_passages.docid: 42145
negative_passages.text: Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.
negative_passages.docid: 26563
negative_passages.text: Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
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: 78117
negative_passages.text: Closed property of nonempty finite set
negative_passages.docid: 117508
negative_passages.text: Prove that the closed unit ball of $L^2[a,b]$ is closed in $L^1[a,b]$
negative_passages.docid: 14711
negative_passages.text: set theoretic function, products of sets (product versus Cartesian product)
negative_passages.docid: 40162
negative_passages.text: Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
negative_passages.docid: 44623
negative_passages.text: Closed set as a countable intersection of open sets
negative_passages.docid: 125962
negative_passages.text: The set $A'$ is closed in a $T_1$ space