query: The set of continuous functions on $[0,1]$ is a vector space.
positive_passages.docid: 26989
positive_passages.text: Show that C[0,1] is a vector space
negative_passages.docid: 52922
negative_passages.text: let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
negative_passages.docid: 55238
negative_passages.text: Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 113687
negative_passages.text: $f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
negative_passages.docid: 14896
negative_passages.text: Prove: the set of zeros of a continuous function is closed.
negative_passages.docid: 23728
negative_passages.text: Does a continuous and 1-1 function map Borel sets to Borel sets?
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 58597
negative_passages.text: A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
negative_passages.docid: 87239
negative_passages.text: Prove functions defined by sup and inf are continuous
negative_passages.docid: 40209
negative_passages.text: $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
negative_passages.docid: 143174
negative_passages.text: property of continuous function
negative_passages.docid: 84512
negative_passages.text: The preimage of continuous function on a closed set is closed.
negative_passages.docid: 83461
negative_passages.text: Continuous iff composition with every linear functional is continuous
negative_passages.docid: 36149
negative_passages.text: A uniformly continuous function maps bounded set to bounded sets
negative_passages.docid: 78344
negative_passages.text: Nonconstant linear functional on a topological vector space is an open mapping
negative_passages.docid: 77621
negative_passages.text: Continuity of function mapping connected set to connected set