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Krein–Milman theorem [6] — If is a compact subset of a Hausdorff locally convex topological vector space then the set of extreme points of has the same closed convex hull as . In the case where the compact set K {\displaystyle K} is also convex, the above theorem has as a corollary the first part of the next theorem, [ 6 ] which is also ...
Most commonly X is called locally compact if every point x of X has a compact neighbourhood, i.e., there exists an open set U and a compact set K, such that . There are other common definitions: They are all equivalent if X is a Hausdorff space (or preregular).
A totally bounded set can be covered by finitely many subsets of every fixed “size” (where the meaning of “size” depends on the structure of the ambient space). The term precompact (or pre-compact) is sometimes used with the same meaning, but precompact is also used to mean relatively compact.
In a press release from November, Amazon outlined how Amazon Haul will work: The mobile-only platform can be accessed via the existing Amazon Shopping app, where consumers will find a selection of ...
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The embedding of X into Y is a compact operator: any bounded set in X is totally bounded in Y, i.e. every sequence in such a bounded set has a subsequence that is Cauchy in the norm ||•|| Y. If Y is a Banach space, an equivalent definition is that the embedding operator (the identity) i : X → Y is a compact operator.
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