query: On which open set $f$ admits an inverse?
positive_passages.docid: 65753
positive_passages.text: The Function $f:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ defined by $f(r,\theta)=(r\cos\theta,r\sin\theta)$
negative_passages.docid: 109046
negative_passages.text: Is the complement of an open ball in a Banach space connected?
negative_passages.docid: 72468
negative_passages.text: Open and closed balls in $C[a,b]$
negative_passages.docid: 150274
negative_passages.text: Inverse of a function - $f^-(x)$ in a restricted domain
negative_passages.docid: 129081
negative_passages.text: Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
negative_passages.docid: 24050
negative_passages.text: Characterization of the Closure of a Set
negative_passages.docid: 132287
negative_passages.text: Axiom of Choice and Right Inverse
negative_passages.docid: 110014
negative_passages.text: Right Inverse for Surjective Function
negative_passages.docid: 154230
negative_passages.text: In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists
negative_passages.docid: 152193
negative_passages.text: The intersection of a closure with an open set
negative_passages.docid: 127900
negative_passages.text: Interior of closure of open set in topological space
negative_passages.docid: 106971
negative_passages.text: Let $f:U \to V$ be a bijective holomorphic function. Show that inverse of $f$ is also holomorphic.
negative_passages.docid: 93040
negative_passages.text: $f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki
negative_passages.docid: 13193
negative_passages.text: Does a inverse function need to be either surjective or injective?
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: 16034
negative_passages.text: Function whose inverse is also its derivative?
negative_passages.docid: 107160
negative_passages.text: Open Set and Measure Theory