query: Are homotopy-preserving maps continuous?
positive_passages.docid: 156996
positive_passages.text: Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$?
negative_passages.docid: 152328
negative_passages.text: A continuously differentiable map is locally Lipschitz
negative_passages.docid: 147788
negative_passages.text: Why is every map to an indiscrete space continuous?
negative_passages.docid: 77944
negative_passages.text: Injective functions with intermediate-value property are continuous. Better proof?
negative_passages.docid: 33129
negative_passages.text: A linear map $S:Y^*\to X^*$ is weak$^*$ continuous if and only if $S=T^*$ for som $T\in B(X,Y)$
negative_passages.docid: 76351
negative_passages.text: Equivalence of continuity definitions
negative_passages.docid: 145077
negative_passages.text: A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
negative_passages.docid: 155618
negative_passages.text: Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
negative_passages.docid: 43874
negative_passages.text: Differentiability implies continuity - A question about the proof
negative_passages.docid: 91337
negative_passages.text: Is every self-homeomorphism homotopic to a diffeomorphism?
negative_passages.docid: 77621
negative_passages.text: Continuity of function mapping connected set to connected set
negative_passages.docid: 154751
negative_passages.text: $f$ brings convergent nets to convergent nets, is it continuous?
negative_passages.docid: 23965
negative_passages.text: Function which preserves closed-boundedness and path-connectedness continuous?
negative_passages.docid: 124829
negative_passages.text: Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell
negative_passages.docid: 32359
negative_passages.text: Inner product of two continuous maps is continuous
negative_passages.docid: 73559
negative_passages.text: Map preserving intervals but discontinuous
negative_passages.docid: 107148
negative_passages.text: Does there always exist a continuous/smooth map from $\mathbb{R}^n$ onto a manifold $M^n$?