query: set of continuous ponits of bounded function is borel
positive_passages.docid: 157384
positive_passages.text: Points of continuity is a Borel set?
negative_passages.docid: 138768
negative_passages.text: Showing that the family of Borel sets is countably generated
negative_passages.docid: 121079
negative_passages.text: lemma: Cauchy sequences are bounded.
negative_passages.docid: 47419
negative_passages.text: Asymptotics of uniformly continuous functions over $\mathbb R$
negative_passages.docid: 36166
negative_passages.text: Uniform continuity on (0,1) implies boundedness
negative_passages.docid: 12349
negative_passages.text: a construction of a continuous function from a normal space to [0,1]
negative_passages.docid: 139612
negative_passages.text: Follow-up regarding right-continuous $f:\mathbb{R} \to\mathbb{R}$ is Borel measurable
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval
negative_passages.docid: 84512
negative_passages.text: The preimage of continuous function on a closed set is closed.
negative_passages.docid: 130975
negative_passages.text: Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
negative_passages.docid: 115878
negative_passages.text: Continuous unbounded but integrable functions
negative_passages.docid: 99117
negative_passages.text: Existence of a sequence of positive continuous functions on $\mathbb R$ which is unbounded precisely on $\mathbb Q$
negative_passages.docid: 83046
negative_passages.text: A linear map, continuous at zero, is bounded
negative_passages.docid: 64487
negative_passages.text: Continuous function and dense set
negative_passages.docid: 96099
negative_passages.text: Every function on $\mathbb{R}^n$ that is continuous in each variable separately is Borel measurable.
negative_passages.docid: 11082
negative_passages.text: Borel-Cantelli Lemma "Corollary" in Royden and Fitzpatrick
negative_passages.docid: 25306
negative_passages.text: A countable family of point-wise bounded functions defined on finite measurable set is actually uniformly bounded on a closed subset