2 Let W be a

closed subset of a smooth manifold M which has been decomposed into a finite union of locally

closed subsetsAssume 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 of X.

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 of X.

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 of R.

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.