query: Is C_b((a,b)) a complete metric space?
positive_passages.docid: 132491
positive_passages.text: How to show that $C=C[0,1]$ is a Banach space
negative_passages.docid: 118328
negative_passages.text: Metric space is totally bounded iff every sequence has Cauchy subsequence
negative_passages.docid: 3751
negative_passages.text: Proving a distance between molecules defines a metric space.
negative_passages.docid: 140124
negative_passages.text: The distance function on a metric space
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 157753
negative_passages.text: Show that any set in a metric space can be written as the intersection of open sets
negative_passages.docid: 35652
negative_passages.text: Every compact metric space is complete
negative_passages.docid: 144353
negative_passages.text: A closed ball in a metric space is closed
negative_passages.docid: 15365
negative_passages.text: Proving that the triangle inequality holds for a metric on $\mathbb{C}$
negative_passages.docid: 154978
negative_passages.text: Some equivalent formulations of compactness of a metric space
negative_passages.docid: 112303
negative_passages.text: Distances between closed sets on metric spaces
negative_passages.docid: 95831
negative_passages.text: Compactness and sequential compactness in metric spaces
negative_passages.docid: 7402
negative_passages.text: Showing a compact metric space has a countable dense subset
negative_passages.docid: 116069
negative_passages.text: Is every metric space a subspace of some connected metric space?
negative_passages.docid: 74312
negative_passages.text: If Y is complete then B(X,Y) is complete
negative_passages.docid: 80276
negative_passages.text: Metric Space & Cauchy Sequence
negative_passages.docid: 121359
negative_passages.text: Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.