query: Surjective function on a compact metric space
positive_passages.docid: 27517
positive_passages.text: Isometry in compact metric spaces
negative_passages.docid: 26794
negative_passages.text: Metrizability of Hausdorff continuous image of compact 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: 74453
negative_passages.text: Injective and Surjective Functions
negative_passages.docid: 154978
negative_passages.text: Some equivalent formulations of compactness of a metric space
negative_passages.docid: 133504
negative_passages.text: Suppose $X$ is a metric space and $S \subseteq X.$ Then, $S^o=\{x \in X~|~dist(x,S^c)>0\}$.
negative_passages.docid: 21707
negative_passages.text: Constructing a Bijective function via an injective and surjective one.
negative_passages.docid: 115794
negative_passages.text: When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
negative_passages.docid: 16092
negative_passages.text: How to prove that the composition of two surjective functions is surjective
negative_passages.docid: 69528
negative_passages.text: Metrizability of quotient spaces of metric spaces
negative_passages.docid: 126944
negative_passages.text: Metric spaces problem
negative_passages.docid: 128894
negative_passages.text: About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
negative_passages.docid: 73154
negative_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 14509
negative_passages.text: Contraction Map on Compact Normed Space has a Fixed Point
negative_passages.docid: 63146
negative_passages.text: Proof of properties of injective and surjective functions.
negative_passages.docid: 70106
negative_passages.text: diameter on a compact metric space
negative_passages.docid: 138607
negative_passages.text: Proof that a limit point compact metric space is compact.