Recent content by ibdsm

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    Learn Riemannian Geometry: Resources for Self-Learners

    If you lack the rigour to study Riemannian geometry comfortably, try working through Spivak's "Calculus on Manifolds". It is the single book I would recommend for studying multivariate calculus, and it paves the way to differential and Riemannian geometry.
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    Can open sets and closures intersect in a topological space?

    I'm glad I'm not the only one to blunder at times!
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    Fundamental theorem of calculus for surface integrals?

    Stokes Theorem connects (n+1)-fold integrals over a region with n-fold integrals over the boundary of the region. The fundamental theorem of calculus is the case n=0. (An integral over a discrete set is a sum - use counting measure)
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    Can open sets and closures intersect in a topological space?

    1. [1,0] is the empty set, as there are no real numbers which are both at least 1 and at most 0. Hence your "counter-example" fails. 2. By definition, (i) a subset of a topological space is closed if and only if it is the complement of an open set (ii) the closure of a subset...
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    Can open sets and closures intersect in a topological space?

    A \cap B empty If A and B are disjoint, the B is a subset of the complement of A. If A is open, its complement is closed. Hence, in this case, the closure of B is contained in the complement of A. Hence, A and the closure of B are disjoint. There is no need for the ambient space to...
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    Where do I start with self learning linear algebra

    In my view, no better place to start than Klaus Jänich's "Linear Algebra". This is the translation into English of one of the common textbooks for the first semester of first year at German universities for students studying maths and/or physics. It is thoroughly modern in its approach. The...
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