query: Spaces whose all their metrizations are complete
positive_passages.docid: 20164
positive_passages.text: Is there always an equivalent metric which is not complete?
negative_passages.docid: 100362
negative_passages.text: Codomain of function complete implies function space complete
negative_passages.docid: 81929
negative_passages.text: d-metrizable spaces are sequential
negative_passages.docid: 108619
negative_passages.text: Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty
negative_passages.docid: 136108
negative_passages.text: Arbitrary intersection of closed, connected subsets of a compact space connected?
negative_passages.docid: 92526
negative_passages.text: Collection of clopen sets form a base for a countable completely regular space
negative_passages.docid: 89468
negative_passages.text: Space Sobolev $W^{m,p}$ complete
negative_passages.docid: 44457
negative_passages.text: Why we define the completeness of a space by the converge of a Cauchy sequence rather than a normal sequence?
negative_passages.docid: 6210
negative_passages.text: Countable compact spaces as ordinals
negative_passages.docid: 119105
negative_passages.text: If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
negative_passages.docid: 134601
negative_passages.text: whether they are complete metric space
negative_passages.docid: 70017
negative_passages.text: Every subspace of a compact space is compact?
negative_passages.docid: 155621
negative_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 36237
negative_passages.text: Closed set mapped to itself in a compact Hausdorff space
negative_passages.docid: 48557
negative_passages.text: Product of connected spaces
negative_passages.docid: 144731
negative_passages.text: Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
negative_passages.docid: 125610
negative_passages.text: Space of bounded continuous functions is complete