query: Closed graph theorem( metric spaces)
positive_passages.docid: 149820
positive_passages.text: How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed?
negative_passages.docid: 11455
negative_passages.text: Connected metric spaces with at least 2 points are uncountable.
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 113022
negative_passages.text: Is the graph $G_f=\{(x,f(x)) \in X \times Y\ : x \in X \}$ a closed subset of $X \times Y$?
negative_passages.docid: 123061
negative_passages.text: $X$ metric separable then $C(X)$ separable
negative_passages.docid: 28804
negative_passages.text: No. of possible dense subsets of a metric space
negative_passages.docid: 144353
negative_passages.text: A closed ball in a metric space is closed
negative_passages.docid: 52014
negative_passages.text: Showing $(C[0,1], d_1)$ is not a complete metric space
negative_passages.docid: 95831
negative_passages.text: Compactness and sequential compactness in metric spaces
negative_passages.docid: 35573
negative_passages.text: A closed ball in a metric space is a closed set
negative_passages.docid: 137881
negative_passages.text: A not complete metric space?
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: 146485
negative_passages.text: Prove that the product space is a metric space.
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: 59654
negative_passages.text: Show that in a discrete metric space, every subset is both open and closed.
negative_passages.docid: 36566
negative_passages.text: Equivalence classes and metric spaces
negative_passages.docid: 16060
negative_passages.text: Showing this metric space is complete