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  • Two definitions of a morphism (locally) of finite type
    Conversely, I do not know whether a the Stacks project's definition of a morphism of finite type (i e locally of finite type and quasi-compact) implies Hartshorne's definition of a morphism of finte type
  • What makes a space locally Euclidean Euclidean?
    As said below, this is largely a terminological matter However, if you care about the "locally Euclidean-ness" of a manifold allowing for locally defined metric features, when your locally Euclidean space is second-countable and Hausdorff, then you can define a metric on it which does what you expect it to
  • general topology - Definition of locally connected topological space . . .
    A topological space is locally connected if every point admits a neighbourhood basis consisting of open connected sets To the definition given by Lee (Introduction to topological manifolds - page $92$) which sums up definitions $1$ and $2$ more "compactly" as follows;
  • Exact meaning of every 2d manifold is locally conformal flat
    The definition is given in the third paragraph on the Wikipedia article (also see the following paragraph for differences in naming) Note that local conformal flatness is a property of Riemannian manifold, so you need to specify a Riemannian metric Amazingly, every 2-dimensional Riemannian manifold is locally conformally flat - this is the theorem you are referring to
  • Terminology for local contractibility: locally contractible vs . . .
    I'm working on formalizing locally contractible spaces in Mathlib (the mathematics library for the Lean theorem prover), and I've encountered conflicting terminology in the literature regarding local contractibility
  • general topology - Definition of a locally Euclidean space . . .
    Yes, that is exactly what it means In general, we often suppress mention of the subspace topology when referring to a set as a topological space if that set is a subset of exactly one topological space considered so far





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