query: Vector space of all real-valued continuous function over $[a,b]$
positive_passages.docid: 17495
positive_passages.text: Show that the vector space of all continuous real-valued functions is infinite-dimensional
negative_passages.docid: 135661
negative_passages.text: Weakly continuous operators are continuous
negative_passages.docid: 15487
negative_passages.text: Continuous function from a connected set?
negative_passages.docid: 36150
negative_passages.text: Ideal in a ring of continuous functions
negative_passages.docid: 86362
negative_passages.text: Cyclic vectors in a real vector space
negative_passages.docid: 100839
negative_passages.text: If two continuous functions are equal almost everywhere on $[a,b]$, then they are equal everywhere on $[a,b]$
negative_passages.docid: 29126
negative_passages.text: Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
negative_passages.docid: 64619
negative_passages.text: Continuity of a function of product spaces
negative_passages.docid: 72644
negative_passages.text: Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
negative_passages.docid: 61220
negative_passages.text: What does "$\mathbb{F^n}$ is a vector space over $\mathbb{F}$" mean?
negative_passages.docid: 143174
negative_passages.text: property of continuous function
negative_passages.docid: 125610
negative_passages.text: Space of bounded continuous functions is complete
negative_passages.docid: 43503
negative_passages.text: Bases of complex vector spaces and the axiom of choice
negative_passages.docid: 9320
negative_passages.text: Extension of continuous function on a closed subset of $\mathbb{R}$
negative_passages.docid: 2142
negative_passages.text: Finding a set of continuous functions with a certain property 2
negative_passages.docid: 81229
negative_passages.text: Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
negative_passages.docid: 53850
negative_passages.text: Proof that every normed vector space is a topological vector space