query: How to prove that the closed unit ball in $\mathbb{R}^n$, with the subspace topology, is not a manifold?
positive_passages.docid: 143254
positive_passages.text: Closed ball not a manifold.
negative_passages.docid: 122352
negative_passages.text: Topologies in a Riemannian Manifold
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 150987
negative_passages.text: Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
negative_passages.docid: 41047
negative_passages.text: Subspace Topology of a subset
negative_passages.docid: 82474
negative_passages.text: Isometries of $\mathbb{R}^n$
negative_passages.docid: 12467
negative_passages.text: Why does this proof work: Closed unit ball in $C_0$ is not compact
negative_passages.docid: 120623
negative_passages.text: Unit sphere in $\mathbb{R}^\infty$ is contractible?
negative_passages.docid: 151425
negative_passages.text: Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
negative_passages.docid: 136592
negative_passages.text: Examples of manifolds that are not boundaries
negative_passages.docid: 80100
negative_passages.text: Boundary of product manifolds such as $S^2 \times \mathbb R$
negative_passages.docid: 35305
negative_passages.text: Why is $\mathbb{R}^2$ not a subset and /or a subspace of $\mathbb{R}^3$?
negative_passages.docid: 138653
negative_passages.text: Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
negative_passages.docid: 39114
negative_passages.text: Prove that a set in $\mathbb R^3$ is not an algebraic set
negative_passages.docid: 99675
negative_passages.text: A closed ball in $l^{\infty}$ is not compact
negative_passages.docid: 115272
negative_passages.text: Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
negative_passages.docid: 73248
negative_passages.text: Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group