query: Show that the metric space C[a,b] is complete.
positive_passages.docid: 132491
positive_passages.text: How to show that $C=C[0,1]$ is a Banach space
negative_passages.docid: 143674
negative_passages.text: Space of bounded functions is complete
negative_passages.docid: 42266
negative_passages.text: Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
negative_passages.docid: 66550
negative_passages.text: Cardinality of separable metric spaces
negative_passages.docid: 83159
negative_passages.text: Defining a metric space
negative_passages.docid: 125580
negative_passages.text: Proving that every countable metric space is disconnected?
negative_passages.docid: 50677
negative_passages.text: Is this metric space incomplete?
negative_passages.docid: 133152
negative_passages.text: (X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.
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: 140692
negative_passages.text: Existence of a complete metric on $(0,1)$
negative_passages.docid: 26563
negative_passages.text: Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
negative_passages.docid: 150987
negative_passages.text: Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
negative_passages.docid: 125610
negative_passages.text: Space of bounded continuous functions is complete
negative_passages.docid: 84264
negative_passages.text: the space of lipschitz function is complete with respect to some norm
negative_passages.docid: 154978
negative_passages.text: Some equivalent formulations of compactness of a metric space
negative_passages.docid: 99645
negative_passages.text: Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
negative_passages.docid: 150011
negative_passages.text: Proof completeness of $(X,d)$ given $d$ is French railway metric