Sentence examples for the space is compact. from inspiring English sources

If the space is compact (for example, a closed and bounded subset of Euclidean space such as Poincaré had considered, but the concept is much more general) and the transformation is continuous, then the recurrence theorem holds.

The space is compact: to the left, a row of chafing dishes; at the back, two giant rice cookers dwarfing a sink scaled for a child's play kitchen; and in the middle, Saeed Pourkay, beaming in his crimson chef's coat.

(Continuumwise connectedness implies connectedness; the converse is true if the space is compact Hausdorff).

bIn the real case, when the state space is compact, then the existence follows from the compactness of the set of all probability measures (i.e., Prohorov's Theorem).

Assuming that the extreme boundary of the trace space is compact and finite dimensional, and that the induced action on the trace space is trivial, we show that strongly outer Z-actions have finite Rokhlin dimension in the sense of Hirshberg, Winter and Zacharias.

Additionally, if A has strict comparison of positive elements, it is known that the Cuntz semigroup of this C*-algebra is recovered functorially from the Murray von Neumann semigroup and the tracial state space whenever the extreme boundary of the tracial state space is compact and of finite covering dimension.

This has led to a good understanding of such things as complex homomorphisms and ideals (but not subalgebras) when the underlying metric space is compact.

Notice that nonempty bounded closed and convex subset of a reflexive Banach space is compact in the weak topology.

Even his work space is compact: one 12-by-12-inch 12-by-12-inch 12-by-12-inch 12-by-12-inchh in the basement of his house in Locust Valley.

A fuzzy metric space is compact if every sequence in X has a convergent subsequence.

(d) A fuzzy metric space is compact if every sequence in X has a convergent subsequence.  .