query: How to prove the uniqueness of a continuous extension of a densely defined function?
positive_passages.docid: 24083
positive_passages.text: $f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$
negative_passages.docid: 130023
negative_passages.text: Prove that the sum of two continuous functions is continuous
negative_passages.docid: 116732
negative_passages.text: Proving that a continuous map is surjective
negative_passages.docid: 62048
negative_passages.text: Proving a Lipschitz function is continuous
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: 135772
negative_passages.text: how to show image of a non constant entire function is dense in $\mathbb{C}$?
negative_passages.docid: 40576
negative_passages.text: Intermediate value property problem and continuous function
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: 140212
negative_passages.text: Prove that there exists a unique linear map that extends the map from a basis
negative_passages.docid: 115878
negative_passages.text: Continuous unbounded but integrable functions
negative_passages.docid: 61122
negative_passages.text: A continuous mapping is determined by its values on a dense set
negative_passages.docid: 80559
negative_passages.text: In $C[0,1]$ prove that the subset of Lipschitz functions is dense
negative_passages.docid: 146306
negative_passages.text: A continuous surjective function from $(0,1]$ onto $[0,1]$
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: 128911
negative_passages.text: Continuous extension of a real function
negative_passages.docid: 125682
negative_passages.text: Proof verification: the product of two continuous functions is continuous
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?