Thus, a manifold has a handle decomposition with only " 0 "-handles if it is diffeomorphic to a disjoint union of balls.
42.
It follows that a locally connected space " X " is a topological disjoint union \ coprod C _ x of its distinct connected components.
43.
For any cardinal number K, the K-hedgehog space is formed by taking the disjoint union of K real unit intervals identified at the origin.
44.
In other words, if is the set of all th roots of unity and is the set of primitive ones, is a disjoint union of the:
45.
Then any smooth separated scheme of finite type over " k " is a finite disjoint union of smooth varieties over " k ".
46.
But in Boole's original system, + was a partial operation : in the language of set theory it would correspond only to disjoint union of subsets.
47.
That is, the free product plays the same role in group theory that disjoint union plays in set theory, or that the direct sum plays in module theory.
48.
That is, it is a functor whose value on a disjoint union of manifolds is equivalent to the tensor product of its values on each of the constituent manifolds.
49.
Another case of this abstract notion of partial trace takes place in the category of finite sets and bijections between them, in which the monoidal product is disjoint union.
50.
In particular, every uncountable Polish space has the perfect set property, and can be written as the disjoint union of a perfect set and a countable open set.
