query: Nonempty sets in $\mathcal{B} ( \mathbb{R}^{[0, \infty)})$ are not contained in the set of continuous functions
positive_passages.docid: 146707
positive_passages.text: Formally show that the set of continuous functions is not measurable
negative_passages.docid: 98772
negative_passages.text: Continuity of a function in $\mathbb{R}$
negative_passages.docid: 100919
negative_passages.text: Examples of non-measurable sets in $\mathbb{R}$
negative_passages.docid: 140445
negative_passages.text: Sequence of continuous functions whose pointwise limit is discontinuous
negative_passages.docid: 6675
negative_passages.text: Lebesgue measurable set that is not a Borel measurable set
negative_passages.docid: 3896
negative_passages.text: A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
negative_passages.docid: 64487
negative_passages.text: Continuous function and dense set
negative_passages.docid: 95635
negative_passages.text: $\ell^{\infty}(\mathbb N)$ is not a separable space
negative_passages.docid: 90826
negative_passages.text: Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
negative_passages.docid: 51156
negative_passages.text: Function is Continuous When Restricted to Closed Sets Which Cover the Space
negative_passages.docid: 62793
negative_passages.text: $\mathbb{R}$ with the lower limit topology is not second-countable
negative_passages.docid: 88099
negative_passages.text: Not $\sigma$-compact set without axiom of choice
negative_passages.docid: 14516
negative_passages.text: The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
negative_passages.docid: 134983
negative_passages.text: Borel sigma algebra not containing all subsets of $\mathbb{R}$?
negative_passages.docid: 74330
negative_passages.text: $\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
negative_passages.docid: 102250
negative_passages.text: Subset of $C[0,1]$ is nowhere dense
negative_passages.docid: 99675
negative_passages.text: A closed ball in $l^{\infty}$ is not compact