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locally    音标拼音: [l'okəli]
ad. 地方性地,局部性地,位置上



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  • general topology - Two definitions of locally compact space . . .
    Every locally compact, second countable Hausdorff space has a countable basis of open sets with compact closure 1 Confusion about definition of locally compact topological space
  • What are presentable categories? - Mathematics Stack Exchange
    I will speak about $\mathbf{Cat}$ as an ordinary locally small category There is no significant difference between the the various notions because filtered colimits in $\mathbf{Cat}$ preserve equivalences, and so a category is finitely presentable in the bicategorical sense if and only if it is equivalent to one that is finitely presentable in the enriched sense, and because the 2-categorical
  • Is connected component open? - Mathematics Stack Exchange
    There is a theorem that:A space is locally connected iff each connected components of an open set is open But recently I had seen to prove That each connected component is closed Connected Components are Closed Then how can the connected component of an open set be open if it is a locally connected space ?
  • abstract algebra - Locally Noetherian schemes are quasiseparated . . .
    $\begingroup$ It is better if you know that every affine open of a locally Noetherian scheme is the spectrum of a Noetherian ring That way you are not stuck with just the given covering $\mathrm{Spec}(A_i)$ $\endgroup$
  • 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
  • calculus - Is locally linear an appropriate description of a . . .
    I think there is a big difference between "locally linear" and other uses of "locally" For instance, "locally compact", "locally connected" means, (essentially, or implies) that every point has a neighborhood which IS compact connected "Locally Euclidean" means that every point has a neighborhood which IS $\mathbb
  • Locally compact metric space - Mathematics Stack Exchange
    So any incomplete locally compact metric space is a counter-example to "only if" Moreover, as mentioned Tsemo Aristide's answer, any non-compact metric space, even a proper one, has the same topology as some improper metric space A normed space X is proper iff it is locally bounded (iff it is finite-dimensional)
  • general topology - Definition of a locally Euclidean space . . .
    Let's say we want a general notion of "$(X,\tau)$ is locally homeomorphic to $(Y,\sigma)$ " In general, $(Y,\sigma)$ may not have the same "self-similarity" property of $\mathbb{R}^n$ which makes the two definitions of "locally Euclidean" equivalent So we get two inequivalent candidates for a general notion of "locally homeomorphic" here
  • general topology - What is the relationship between completeness and . . .
    Every locally compact metric space will be an open subset of its completion, and every G$_\delta$ subset of a complete metric space is completely metrizable Every locally compact completely regular space is Čech-complete ( i e , is a G$_\delta$ subset of its Stone-Čech (or any other) compactification), and a metric space is completely





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