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.