Then any compact closed map F [member of] B(X, X) has a fixed point.

E and F [member of] B(X, X) a compact closed map. Then F has a fixed point.

(2) If F : E [??] Z is a closed map such that F[[phi].sub.N] [member of] KC([[DELTA].sub.n], Z) for any N [member of] <D> with the cardinality [absolute value of (N)] = n + 1, then F [member of] B(E, Z).

Then any compact closed map F [member of] KC(X, X) has a fixed point.

Definition 1: A map f:X[right arrow]Y is called a pre [alpha] g* closed map if f(A) is [alpha] g* closed in Y whenever A is [alpha] g* closed in X.

Theorem 1: Every homeomorphism is a pre [alpha] g* closed map.

Therefore f is a pre [alpha] g* closed map.{b} is closed in (X,[T.sub.2]) [f.sup.-1] (b) = {b} is not closed in (X,[T.sub.1]).

By this definition, [theta] is an open and

closed map. Therefore, each closed subset of [??] has the form

Balachandran, Semi-generalized

closed maps and Generalized semi-

closed maps, Mem.

Let S be the semigroup of all

closed maps like f : X [right arrow] X, under composition of maps:

Balachandran: Semi-generalised closed maps and generalised semi-closed maps, Mem.

Balachandran: Generalised [alpha]-closed maps and [alpha]-generalised closed maps, Indian J.