query: Every compact metric space is complete, proof verification
positive_passages.docid: 35652
positive_passages.text: Every compact metric space is complete
negative_passages.docid: 6785
negative_passages.text: Equicontinuity on a compact metric space turns pointwise to uniform convergence
negative_passages.docid: 137881
negative_passages.text: A not complete metric space?
negative_passages.docid: 28391
negative_passages.text: Prove the compactness of a set B
negative_passages.docid: 134601
negative_passages.text: whether they are complete metric space
negative_passages.docid: 95831
negative_passages.text: Compactness and sequential compactness in metric spaces
negative_passages.docid: 52104
negative_passages.text: A pseudometric on the space of the measurable functions is complete
negative_passages.docid: 73368
negative_passages.text: Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
negative_passages.docid: 135157
negative_passages.text: Totally bounded, complete $\implies$ compact
negative_passages.docid: 29744
negative_passages.text: Compactness and axiomatisability
negative_passages.docid: 36566
negative_passages.text: Equivalence classes and metric spaces
negative_passages.docid: 123061
negative_passages.text: $X$ metric separable then $C(X)$ separable
negative_passages.docid: 114061
negative_passages.text: Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
negative_passages.docid: 111119
negative_passages.text: Distance between any two points in a compact metric space
negative_passages.docid: 125580
negative_passages.text: Proving that every countable metric space is disconnected?
negative_passages.docid: 94485
negative_passages.text: Limit point compactness implies compactness.
negative_passages.docid: 126944
negative_passages.text: Metric spaces problem