Suppose, moreover, that X is a closed, infinite,

proper subset of T that is invariant with respect to F.

If X cannot be expressed as the union of two disjoint sets A([not equal to] 0) and B([not equal to] 0) such that A is [[tau].sub.1]-[delta] semiopen and B is [[tau].sub.2]-[delta] semiopen, then X does not contain any nonempty

proper subset which is both [[tau].sub.1]-[delta] semiopen and [[tau].sub.2]-[delta] semiclosed.

Hence [G.sub.[alpha]] is non-empty

proper subset of X which is [alpha]-closed as well [alpha]-open.

If A(I) does not contain a

proper subset which is a BCI/BCK-algebra, then A(I) is called a pseudo neutrosophic subalgebra of X(I).

(2) (U; C) has no nonempty definable

proper subset.

If B is a maximum distribution set, and no

proper subset of B is a maximum distribution consistent set, then B is called a maximum distribution consistent reduction of [J.sup.[greater than or equal to]].

A Boolean-near-ring (B, [disjunction], [and]) is having the

proper subset A, is a maximal set with uni-element in an associate ring R, with identity under suitable definitions for (B, +,) with corresponding lattices (A, [less than or equal to])(A, <) and

According to the subset account of realization, a property, F, is realized by another property, G, whenever F is individuated by a nonempty

proper subset of the causal powers by which G is individuated (and F is not a conjunctive property of which G is a conjunct).

If T is a transversal in H and if no

proper subset of T is a transversal in H, then T is called a minimal transversal in H.

The essential properties of a thing form a

proper subset of its metaphysically necessary properties.

Super Niven numbers are infinitely many (again, look at powers of 10) and they form a

proper subset of the Niven numbers.

Then {[V.sub.[alpha]]: [alpha][member of][[DELTA].sub.2]} is a ([[tau].sub.j], [[tau].sub.i])- regularly closed cover of the ([[tau].sub.j], [[tau].sub.i])- regularly open

proper subset [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

I would have to say this because you have to have one element from C to be a

proper subset at all.

To answer the latter question first, the types' meaning and extension constitute two ways of establishing the ordering: "in terms of meaning, each type specification is schematic for the one that follows; as for extension, the members of each category include those of the next as the

proper subset" (Langacker 1991: 61).6 Depending on the perspective taken, then, the relationship between a type and a subtype (e.g., between mammal and squirrel), appears to be, on the one hand, a relation of schematicity (and, by the same token it reduces to "precision of specification" (Langacker 1991:61)), and on the other hand, a kind of inclusion relation, which obtains between a subset and a set.

More generally, suppose f : [N.sup.k] [right arrow] N is "almost c.c.," in the sense that if h is any function obtained from f by replacing a

proper subset of the variables of f by constants then h is eventually c.c.