query: Definition of boundary of differential manifold is well defined
positive_passages.docid: 155060
positive_passages.text: Confusion about definition of manifold with boundary
negative_passages.docid: 36015
negative_passages.text: Almost complex manifolds are orientable
negative_passages.docid: 148685
negative_passages.text: Equivalences of definitions of submanifolds in $\mathbb{R^n}$
negative_passages.docid: 44194
negative_passages.text: How to show that the unit sphere is a topological manifold?
negative_passages.docid: 102323
negative_passages.text: Nice neighborhoods of each "piece" in a manifold connected sum
negative_passages.docid: 95400
negative_passages.text: Different definitions of exterior derivative
negative_passages.docid: 122410
negative_passages.text: Can one build a homology theory using submanifolds and their boundaries?
negative_passages.docid: 10215
negative_passages.text: Differentiable manifolds as locally ringed spaces
negative_passages.docid: 145937
negative_passages.text: Differential topology versus differential geometry
negative_passages.docid: 152725
negative_passages.text: Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)
negative_passages.docid: 13964
negative_passages.text: Manifold of Density Matrices
negative_passages.docid: 47056
negative_passages.text: Show that the boundary of a set equals the boundary of its complement
negative_passages.docid: 50150
negative_passages.text: Precise definition of the boundary set
negative_passages.docid: 76937
negative_passages.text: Is there an elementary way to see that there is only one complex manifold structure on $R^2$?
negative_passages.docid: 158850
negative_passages.text: Is it true that a boundary of a simply connected and bounded set is connected in $\mathbb{C}$?
negative_passages.docid: 135025
negative_passages.text: Axiomatization of a Topology using the Boundary
negative_passages.docid: 129986
negative_passages.text: Differential Geometry-Wedge product