query: Is a subset of $\mathbb{R}^{n}$ that is homeomorphic to $\mathbb{R}^{n}$ necessarily open?
positive_passages.docid: 144246
positive_passages.text: Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
negative_passages.docid: 47992
negative_passages.text: Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
negative_passages.docid: 2198
negative_passages.text: Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
negative_passages.docid: 60692
negative_passages.text: Is this map to a finite dimensional topological vector space an open map?
negative_passages.docid: 145077
negative_passages.text: A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
negative_passages.docid: 69542
negative_passages.text: Why do the $n \times n$ non-singular matrices form an "open" set?
negative_passages.docid: 15645
negative_passages.text: Is convex open set in $\mathbb{R}^n$ is regular?
negative_passages.docid: 44704
negative_passages.text: familly of Radially open sets in $\mathbb{R}^2$
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 130297
negative_passages.text: $A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
negative_passages.docid: 75829
negative_passages.text: Dimension of open subsets of $R^n$
negative_passages.docid: 108687
negative_passages.text: Open subsets in a manifold as submanifold of the same dimension?
negative_passages.docid: 83446
negative_passages.text: bijective continuous function on $\mathbb R^n$ not homeomorphism?
negative_passages.docid: 39453
negative_passages.text: How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
negative_passages.docid: 149317
negative_passages.text: An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
negative_passages.docid: 83166
negative_passages.text: Homeomorphism(topological spaces) version of Cantor–Bernstein–Schroeder theorem
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$