query: Show that of x is in the closure of a set, then there exists a sequence that converges to x
positive_passages.docid: 24050
positive_passages.text: Characterization of the Closure of a Set
negative_passages.docid: 128482
negative_passages.text: The set of subsequential limits is closed
negative_passages.docid: 21176
negative_passages.text: Closure of the set in dictionary order topology.
negative_passages.docid: 15319
negative_passages.text: Convergence of recurrence sequence
negative_passages.docid: 52711
negative_passages.text: Prove that the sequence $\{v_n\}$ converges to the maximum value of $f$ on $[a,b]$
negative_passages.docid: 10180
negative_passages.text: How to prove that this set is closed?
negative_passages.docid: 66198
negative_passages.text: Sufficient condition for convergence of a real sequence
negative_passages.docid: 87086
negative_passages.text: Equivalence of convergence in products of sequences.
negative_passages.docid: 88610
negative_passages.text: The set of convergence of a sequence of measurable functions is measurable
negative_passages.docid: 77835
negative_passages.text: Proof that injective rearrangements of a convergent sequence preserves its limit
negative_passages.docid: 11586
negative_passages.text: Sequences of Real Numbers in a closed bounded interval
negative_passages.docid: 132140
negative_passages.text: Convergence of Sequence of Real Numbers
negative_passages.docid: 141484
negative_passages.text: Convergence of a sequence by convergence of sub-subsequence
negative_passages.docid: 117764
negative_passages.text: Almost surely convergence of the sequence
negative_passages.docid: 12293
negative_passages.text: Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
negative_passages.docid: 111008
negative_passages.text: Show that $X $ is a infinite set ,it is connected in the finite complement topology?
negative_passages.docid: 133886
negative_passages.text: Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$