query: Extensions of f to a continuous linear functional
positive_passages.docid: 142232
positive_passages.text: Functional Analysis. Continuous extensions of linear functionals.
negative_passages.docid: 155618
negative_passages.text: Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
negative_passages.docid: 44057
negative_passages.text: Pointwise but not uniform convergence of continuous functions on $[0,1]$
negative_passages.docid: 98772
negative_passages.text: Continuity of a function in $\mathbb{R}$
negative_passages.docid: 140445
negative_passages.text: Sequence of continuous functions whose pointwise limit is discontinuous
negative_passages.docid: 47498
negative_passages.text: Integration and theorems on continuous functions
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: 18222
negative_passages.text: Set of continuity points of a real function
negative_passages.docid: 124861
negative_passages.text: The extension of smooth function
negative_passages.docid: 104914
negative_passages.text: Abount linear functional: If $T(B)$ is bounded, is $T$ bounded?
negative_passages.docid: 17223
negative_passages.text: Continuity of an inverse function.
negative_passages.docid: 157269
negative_passages.text: If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
negative_passages.docid: 58816
negative_passages.text: Existence of a continuous function which does not achieve a maximum.
negative_passages.docid: 104257
negative_passages.text: $C^1$ functions on an open connected set and local Lipschitz continuity
negative_passages.docid: 87239
negative_passages.text: Prove functions defined by sup and inf are continuous
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: 141223
negative_passages.text: $f(x^2) = 2f(x)$ and $f(x)$ continuous