# compact set

## compact set

[¦käm‚pakt ′set]
(mathematics)
A set in a topological space with the property that every open cover has a finite subset which is also a cover. Also known as bicompact set.
References in classic literature ?
With this brief introduction, she produced from her pocket an advertisement, carefully cut out of a newspaper, setting forth that in Buckingham Street in the Adelphi there was to be let furnished, with a view of the river, a singularly desirable, and compact set of chambers, forming a genteel residence for a young gentleman, a member of one of the Inns of Court, or otherwise, with immediate possession.
70 loudspeakers, - nurse call compact set, - door intercom with a door station with video and a door station without video.
Since the unit circle is a compact set, by the Tikhonov theorem, the infinitedimensional torus [OMEGA] with the product topology and pointwise multiplication is a compact topological Abelian group.
It is said that a topological linear space Y is Klee admissible if for every compact set K [[subset].bar] Y and for every neighbourhood O of zero in Y there exists a continuous finite-dimensional map L:K [right arrow]Y such that L(y)-y[omega] O for every y[omega]K.
CHX offers trading in more than 8,300 listed securities and offers a compact set of order types designed to provide a level playing field for all order senders.
Then, there exist a unique compact set K and a unique probability measure [mu] on K such that K = [[union].sup.N.sub.i=1] [f.sub.i](K) and
Therefore, the set Uy(t) is closed to an arbitrary compact set. As a result, the set Uy(t) is also relatively compact set in X for t [member of] [0, [infinity]).
For [[OMEGA].sub.1] x [[OMEGA].sub.d] is also compact set, there are nonnegative continuous functions [beta](x) and the maximum of [beta](x) is N.
Now, we consider that [mu] is a probability measure on the compact set X, which is unnecessarily absolutely continuous measure with respect to Lebesgue measure [lambda].
We claim that B = [{[bar.[f.sub.m]]}.sup.[omega]] is a weakly compact set in [W.sup.n,1] ([[0, T].sup.N]).To prove this assertion, we need to check that [mu](B) = 0.
If X is an infinite Talagrand compact set, the weak* dual [L.sub.p]([C.sub.p](X))) of [C.sub.p]([C.sub.p](X))) has a bounded resolution but it has no fundamental bounded resolution.
Then there exists a compact set [PHI] [member of] e(V) [intersection][[PSI].sub.[epsilon]]([eta]).

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