query: Give an example of this strange condition in metric spaces.
positive_passages.docid: 154324
positive_passages.text: preservation of completeness under homeomorphism
negative_passages.docid: 153952
negative_passages.text: A map between metric spaces preserving convergent sequences is continuous
negative_passages.docid: 13848
negative_passages.text: Showing that if a subset of a complete metric space is closed, it is also complete
negative_passages.docid: 36566
negative_passages.text: Equivalence classes and metric spaces
negative_passages.docid: 49503
negative_passages.text: Why does the natural quotient metric works in this case?
negative_passages.docid: 127166
negative_passages.text: Specific example of a space that is separable but not second countable.
negative_passages.docid: 109638
negative_passages.text: Show that a complete metric space without isolated points is uncountable
negative_passages.docid: 140124
negative_passages.text: The distance function on a metric space
negative_passages.docid: 119247
negative_passages.text: Let $(M,d)$ be a compact metric space and $f:M \to M$ such that $d(f(x),f(y)) \ge d(x,y) , \forall x,y \in M$ , then $f$ is isometry?
negative_passages.docid: 27998
negative_passages.text: Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
negative_passages.docid: 80276
negative_passages.text: Metric Space & Cauchy Sequence
negative_passages.docid: 69528
negative_passages.text: Metrizability of quotient spaces of metric spaces
negative_passages.docid: 107321
negative_passages.text: How to show convexity of a ball in metric space?
negative_passages.docid: 140692
negative_passages.text: Existence of a complete metric on $(0,1)$
negative_passages.docid: 18040
negative_passages.text: Show that a compact metric space is bounded
negative_passages.docid: 146485
negative_passages.text: Prove that the product space is a metric space.
negative_passages.docid: 69777
negative_passages.text: Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent