query: Can we drop the requirement of a smooth manifold to be a topological manifold from the definition?
positive_passages.docid: 144548
positive_passages.text: topological structure on smooth manifolds
negative_passages.docid: 51871
negative_passages.text: Characterization of Topology
negative_passages.docid: 44955
negative_passages.text: Can $\mathbb CP^n$ be the boundary of a compact manifold?
negative_passages.docid: 149029
negative_passages.text: 3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps
negative_passages.docid: 77157
negative_passages.text: In GR, why should the spacetime manifold be differentiable?
negative_passages.docid: 132095
negative_passages.text: Motivation for the term "separable" in topology
negative_passages.docid: 27198
negative_passages.text: Not an essential singularity
negative_passages.docid: 107148
negative_passages.text: Does there always exist a continuous/smooth map from $\mathbb{R}^n$ onto a manifold $M^n$?
negative_passages.docid: 26379
negative_passages.text: What is non-manifold geometry?
negative_passages.docid: 55089
negative_passages.text: Basis of the space of vector fields on smooth manifolds
negative_passages.docid: 139827
negative_passages.text: On which topological spaces, can we give a group structure to make it a topological group?
negative_passages.docid: 154009
negative_passages.text: Closed, simply connected manifolds which are not spheres
negative_passages.docid: 64375
negative_passages.text: Non-Metrizable Topological Spaces
negative_passages.docid: 91337
negative_passages.text: Is every self-homeomorphism homotopic to a diffeomorphism?
negative_passages.docid: 80418
negative_passages.text: The "Easiest" non-smoothable manifold
negative_passages.docid: 133808
negative_passages.text: A doubt from Milnor's "Topology from a Differentiable Viewpoint".
negative_passages.docid: 10215
negative_passages.text: Differentiable manifolds as locally ringed spaces