2 Let W be a closed subset
of a smooth manifold M which has been decomposed into a finite union of locally closed subsets
Assume that T is a nonempty closed subset
of R and E is an equivalence relation on T.
A filter on X is said to be closed if it has a base consisting of closed subsets
Let A be a closed subset
of X and B [member of] vGO(X) [contains as member] A [subset or equal to] B.
C], it follow that A [intersection] X contains all closed subset
Proof: Let F be a closed subset
of S and let (x,y) [member of] [sup.
B](b) is a closed subset
in C (see the proof of Proposition 3.
Time scale calculus unifies continuous and discrete calculus and is much more general as T can be any nonempty closed subset
of the reals R.
A time scale T is a nonempty closed subset
of the real numbers, so that it is a complete metric space with the metric d(t, s) = |t - s|.
here B and A are nonnegative numbers, 0, T are points in T, T (the time scale) is a nonempty closed subset
Any I-sequentially closed subset
of a I-sequentially compact subset of X is I-sequentially compact.
i) Let x [member of] X and F be disjoint closed subset
of X not containing x, then f(x) and f(F) are disjoint closed subset
of Y , since f is closed and injection.