Let x [not equal to] y [member of] X, then there are disjoint vg-open sets U, V [member of] vGO(X) [contains as member] x [member of] U and y [member of] V.

3] space if for every vg-closed sets F and a point x [not member of] F, [there exists] disjoint U, V [member of] vO(X) [contains as member] F [subset or equal to] U, x [member of] V;

3] space if for every vg-closed sets F and a point x [not member of] F, [there exists] disjoint U, V [member of] vGO(X) [contains as member] F [subset or equal to] U, x [member of] V;

4] space if for each pair of disjoint vg-closed sets F and H, [there exists] disjoint U, V [member of] vO(X) [contains as member] F [subset or equal to] U, H [subset or equal to] V;

4] space if for each pair of disjoint vg-closed sets F and H, [there exists] disjoint U, V [member of] vgO(X) [contains as member] F [subset or equal to] U, H [subset or equal to] V.

Let Y and Z be disjoint infinite sets and let X = Y [union] Z and [tau] = {[phi], Y, Z, X}.

2] space, x a point in X and C the disjoint v--compact subspace of X not containing x.

2] space, a point and disjoint r-compact subspace can be separated by disjoint v--open sets.

2] space, a point and disjoint semi-compact subspace can be separated by disjoint semi-open sets.

Therefore there exists disjoint open sets U and V in Y such that f(x) [member of] U, f(y) [member of] V, then [f.

3])space at a point x [member of] X if for every closed subset F of X not containing x, there exists disjoint v--open sets G and H such that F [subset] G and x [member of] H.

3] space if for a closed set F and a point x [not member of] F, there exists disjoint v--open sets G and H such that F [subset] G and x [member of] H.