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.
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]).