A

closed subset X of the complex plane is called a spectral set for an operator

Another way to phrase this is a subset S [subset] M is locally closed if and only if it is the intersection of an open subset and a

closed subset of M.

At the beginning a time scale is defined to be an arbitrary

closed subset of the real numbers , with the standard inherited topology.

A family F of closed sets in a space X is separating if S is

closed subset in X and x [member of] S implies there are disjoint sets [F.

Let A be a

closed subset of X and B [member of] [tau](X) [contains as member] A [subset or equal to] B.

Suppose X is a Hausdorff normal topological space, F the algebra generated by the

closed subset of X and [mu]: [C.

1](A) is a

closed subset of S and that f: S [right arrow] S is continous.

A](a) is a

closed subset in c for each a [member of] A with [sp.

Recall that a Hausdorff space is said to be regular if for each

closed subset F of X, p [member of] X\F, there exist disjoint open sets U, V such that p [member of] U, F [subset] V.

Let A be a

closed subset of Y and B be an open set containing A.

A time scale T is an arbitrary nonempty

closed subset of real numbers R.

A time scale is an arbitrary

closed subset of reals, and the cases when this time scale is equal to the reals or to the integers represent the classical theories of differential and difference equations.