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compactness    音标拼音: [kəmp'æktnəs]
紧密度

紧密度

compactness
紧致性

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  • How to understand compactness? - Mathematics Stack Exchange
    Compactness extends local stuff to global stuff because it's easy to make something satisfy finitely many restraints- this is good for bounds Connectedness relies on the fact that ``clopen'' properties should be global properties, and usually the closed' part is easy, whereas the open' part is the local thing we're used to checking
  • What is Compactness and why is it useful? [closed]
    The wiki definiton defines a compactness of an interval as closed and bounded In mathematics, specifically general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (containing all its limit points) and bounded (having all its points lie within some fixed distance of each other)
  • general topology - Difference between completeness and compactness . . .
    Difference between completeness and compactness Ask Question Asked 9 years, 5 months ago Modified 9 years, 5 months ago
  • Understanding compactness and how it relates to finiteness
    It isn't intuitively obvious to me how compactness relates to finiteness, even though I often hear that they are very closely related My definition of compactness is: a set A is compact if, given
  • Compactness and sequential compactness in metric spaces
    Compactness and sequential compactness in metric spaces Ask Question Asked 11 years ago Modified 6 years, 5 months ago
  • Compactness vs Closed and bounded for general metric spaces
    We know that for A ⊂ Rn A ⊂ R n, A is closed bounded A is compact and that this does not generalize to general metric spaces 1 ) For which class of metric spaces, is 'closed bounded' equivalent to compactness Now there is another related question : 2 ) Suppose (X, d) (X, d) is an arbitrary metric space Is it possible to find another metric d′ d ′ such that the induced topologies
  • compactness and boundedness - Mathematics Stack Exchange
    3 Your definition of compactness (closed and bounded) works for R R and Rn R n (and other finite dimensional spaces), but it is not the general definition
  • Why is compactness so important? - Mathematics Stack Exchange
    As many have said, compactness is sort of a topological generalization of finiteness And this is true in a deep sense, because topology deals with open sets, and this means that we often "care about how something behaves on an open set", and for compact spaces this means that there are only finitely many possible behaviors But why finiteness is important? Well, finiteness allows us to
  • compactness sequentially compact - Mathematics Stack Exchange
    I'm looking for two examples: A space which is compact but not sequentially compact A space which is sequentially compact but not compact Explanations why the spaces are compact not compact and
  • general topology - pre-compactness, total boundedness and Cauchy . . .
    Pre-compactness in the first quote is defined differently from the one in the second quote So now my question is narrowed down to whether total boundedness and Cauchy sequential compactness are equivalent in both metric spaces and uniform spaces





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