Let [S.sub.1], [S.sub.2] and [S.sub.3] be three g[ALEPH]

locally compact Hausdorff spaces.

Let X be a

locally compact Hausdorff space and (Y,[[tau].sub.Y]) a topological linear space.

Now, let M(X) be the Banach space of all complex Radon measures on the

locally compact Hausdorff space X with the total variation norm.

Let X be a

locally compact Hausdorff space, and let w : X [right arrow] R be an upper semi-continuous function such that w(t) [greater than or equal to] 1 for every t [member of] X.

-- A topological vector lattice (E,[tau]) is homeomorphic and lattice isomorphic to a dense subspace V of (C(Y),k) for some

locally compact Hausdorff space Y such that V [intersection] [C.sub.[infinity]](Y) is dense in ([C.sub.o](Y), ||*||) if, and only if, (E,[tau]) is an M-partition space.

Let X be a neutrosophic

locally compact Hausdorff space.

For a

locally compact Hausdorff space X we denote by [C.sub.c] (X) the set of all real continuous functions on X with compact support.

In particular, when X is a

locally compact Hausdorff space then using Theorem 1.1, one can observe that [LAMBDA]-closed sets for the hinged set [LAMBDA] [subset or equal to] DP([beta]X, X) are precisely F-compact sets defined by Thrivikraman in [6].

Throughout S denotes a

locally compact Hausdorff topological semigroup.

Concerning the above properties, in the article [1] we proved: (1) If there is a dplb from C(X, V) to C(Y, Z), #X [greater than or equal to] 4, #Y [greater than or equal to] 3, V is linearly isometric to Z and [Z.sup.*] has no isometric copy of ([R.sup.2], [parallel] [[parallel].sub.[infinity]]) then X is homeomorphic to Y; (2) there exist Banach spaces which do not solve the dplb problem; (3) every [C.sub.0](L) space, where L is a

locally compact Hausdorff space, has the dplb property.

Throughout this paper, [??] denotes a locally compact semigroup; i.e., a semigroup with a

locally compact Hausdorff topology whose binary operation is jointly continuous.

Let S denote a locally compact semigroup, that is a semigroup with a

locally compact Hausdorff topology under which the binary operation of S is jointly continuous.