query: On the space of continuous functions of a second-countable space
positive_passages.docid: 17733
positive_passages.text: $X$ second countable locally compact Hausdorff implies $C(X)$ separable?
negative_passages.docid: 125610
negative_passages.text: Space of bounded continuous functions is complete
negative_passages.docid: 148403
negative_passages.text: Compact space and Hausdorff space
negative_passages.docid: 64487
negative_passages.text: Continuous function and dense set
negative_passages.docid: 95321
negative_passages.text: Subspaces of all real-valued continuous functions on $\mathbb{R}^1$
negative_passages.docid: 12003
negative_passages.text: Cardinality of set of real continuous functions
negative_passages.docid: 65346
negative_passages.text: Characterisation of uniformly continuous function
negative_passages.docid: 71001
negative_passages.text: Do continuous linear functions between Banach spaces extend?
negative_passages.docid: 154625
negative_passages.text: $\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
negative_passages.docid: 34836
negative_passages.text: Composition of Absolutely Continuous Functions
negative_passages.docid: 105358
negative_passages.text: In a second countable space any base has a countable subset that is still a base
negative_passages.docid: 158567
negative_passages.text: A uniform continuous function which is not Hölder continuous
negative_passages.docid: 64619
negative_passages.text: Continuity of a function of product spaces
negative_passages.docid: 126759
negative_passages.text: Unbounded continuous function on non-compact metric space
negative_passages.docid: 36149
negative_passages.text: A uniformly continuous function maps bounded set to bounded sets
negative_passages.docid: 135661
negative_passages.text: Weakly continuous operators are continuous
negative_passages.docid: 81933
negative_passages.text: Topological spaces in which a set is the support of a continuous function iff it is the closure of a open set.