query: Dimension is well-defined on each connected component of a manifold
positive_passages.docid: 143929
positive_passages.text: dimension of a connected Manifold
negative_passages.docid: 73172
negative_passages.text: Is every complex (smooth) manifold a scheme?
negative_passages.docid: 108687
negative_passages.text: Open subsets in a manifold as submanifold of the same dimension?
negative_passages.docid: 122410
negative_passages.text: Can one build a homology theory using submanifolds and their boundaries?
negative_passages.docid: 14429
negative_passages.text: dimension of a subspace spanned by two subspaces
negative_passages.docid: 154009
negative_passages.text: Closed, simply connected manifolds which are not spheres
negative_passages.docid: 142097
negative_passages.text: Finding the dimension of the orthogonal complement
negative_passages.docid: 40293
negative_passages.text: Understanding the definition of norm of tensors on a Riemannian manifold
negative_passages.docid: 78624
negative_passages.text: CW complexes and manifolds
negative_passages.docid: 75829
negative_passages.text: Dimension of open subsets of $R^n$
negative_passages.docid: 90092
negative_passages.text: Showing that $\bar{\mathbb{B}}^n$ is a manifold with boundary (Lee ITM Probelm 3-4)
negative_passages.docid: 94215
negative_passages.text: Fundamental group of the connected sum of manifolds
negative_passages.docid: 61816
negative_passages.text: Cut points and connected space
negative_passages.docid: 89264
negative_passages.text: Connectedness in the Quotient Space
negative_passages.docid: 19453
negative_passages.text: Invariance of domain for manifold
negative_passages.docid: 155060
negative_passages.text: Confusion about definition of manifold with boundary
negative_passages.docid: 147961
negative_passages.text: Characterizing simply connected spaces