query: Continuously bijective but not homotopy equivalent.
positive_passages.docid: 19984
positive_passages.text: Example of topological spaces with continuous bijections that are not homotopy equivalent
negative_passages.docid: 118192
negative_passages.text: Is there a bijective function $f: \mathbb{R}\to\mathbb{R}$ that is discontinuous?
negative_passages.docid: 62817
negative_passages.text: Functions which are Continuous, but not Bicontinuous
negative_passages.docid: 107400
negative_passages.text: Can there be an injective function whose derivative is equivalent to its inverse function?
negative_passages.docid: 93358
negative_passages.text: Find an example of a non-surjective field endomorphism
negative_passages.docid: 93776
negative_passages.text: Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
negative_passages.docid: 17607
negative_passages.text: Open maps which are not continuous
negative_passages.docid: 151575
negative_passages.text: Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
negative_passages.docid: 45380
negative_passages.text: Surjectivity implies injectivity and conversely
negative_passages.docid: 14322
negative_passages.text: Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
negative_passages.docid: 44689
negative_passages.text: Explicit bijection between $[0,1)$ and $(0,1)$
negative_passages.docid: 95086
negative_passages.text: Homeomorphism is bijective
negative_passages.docid: 143051
negative_passages.text: Inverting noninvertible elements in a bigger ring.
negative_passages.docid: 57269
negative_passages.text: A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$
negative_passages.docid: 65034
negative_passages.text: Are continuous self-bijections of connected spaces homeomorphisms?
negative_passages.docid: 82675
negative_passages.text: What is an example of function $f: \Bbb{N} \to \Bbb{Z}$ that is a bijection?
negative_passages.docid: 63836
negative_passages.text: Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective