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  • The definition of locally Lipschitz - Mathematics Stack Exchange
    Here's a scan of the first edition of the text, where the only change from the second (latest) edition referred to above is that the last sentence now reads "This is called the local Lipschitz property" (emphasis mine) Two questions: Is the correct inequality M ≥ 0 M ≥ 0 or M> 0 M> 0? Does M M depend on x0 x 0, like δ0 δ 0 seems to?
  • Locally Complete Metric Space - Mathematics Stack Exchange
    The Locally Complete Metric Space is a metric space where each point has a neighbourhood (which is closed) is a complete metric space It is so obvious that every complete metric space is locally complete metric space I am looking for an example of locally complete metric space that is not complete metric space
  • the equivalency of two definitions of locally closed sets
    here there are 2 definitions of locally closed sets: A is locally closed subset of X if: a) every element in A has a neighborhood V in X such that A ∩ V is closed in V b) A is open in its closure (in X) why a) and b) are equivalent?
  • Locally Closed Immersion - Mathematics Stack Exchange
    My question is why does this already imply that ΔX Δ X is a locally closed immersion? Is it a base change argument? I know that (open closed) immersions are stable under base change but does the base change argument work "in another direction"? namely that if P P is a property stable under base change and k: X → Y k: X → Y has P P and l:X′ → X l: X ′ → X is some morphism then Y×
  • Are all manifolds locally flat? - Mathematics Stack Exchange
    Regarding tractability, because any two connected manifolds of the same dimension are locally homeomorphic, dimension is a (topological or smooth) manifold's only local invariant All else is global: compactness, homology and homotopy groups, etc
  • Irreducible components - Mathematics Stack Exchange
    Why the set of irreducible components of a scheme is locally finite? Actually,we know that a noetherian space has only a finitely many irreducible components,but I want to know something more
  • Local freeness in vector bundles and projective modules
    A locally free sheaf is only the same as a locally free module over an affine scheme variety There's no finite presentation condition required A trivialization of a vector bundle is a cover of your space by Zariski open sets such that the restriction of your bundle to each open set in the cover is isomorphic to the trivial vector bundle (of the same rank) The connection with locally free
  • Why do we define partitions of unity to be locally finite instead of . . .
    Henno Brandsma’s answer tells us that in fact pointwise countable partitions give rise to locally finite ones That’s quite cool and relevant, but my question really is about asking what major theorems proofs concepts are easier using the locally finite definition of partitions of unity





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