Let CC (X) ={A [subset.bar] X : A is a non-empty compact convex
subset of X}, WCC (X) ={A [subset.bar] X : A is a non-empty weakly compact, convex
subset of X} and BCC (X) ={A [subset.bar] X : A is a non-empty bounded, closed, convex
subset of X}: Then (CC (X); h) ; (WCC (X); h) and (BCC (X); h) are known as the hyperspaces over the underlying space (X; ||*||).
A
subset X of E is called a [GAMMA]-convex
subset of (E, D; [GAMMA]) relative to some D' [subset] D if, for any N [member of] <D'>, we have [[GAMMA].sub.N] [subset] X, that is, [co.sub.[GAMMA]]D' [subset] X.
The presumption will not apply if the taxpayer "can identify a
subset of elements of dual function software that only enables a taxpayer to interact with third parties or allows third parties to initiate functions or review data (third party
subset)" (Regs.
The food and beverages (non-alcoholic) set carrying a weight of nearly 24% in the CPI basket led the monthly fall with a price slump of 1.36%, which was slightly offset by rising prices of the housing, water, electricity, gas and other fuels
subset (with a weight of over 26%) at 0.03%.
For a
subset A of topological space X, Int(A), Cl(A), [Cl.sub.[alpha]](A) and [Int.sub.[alpha]](A) denote the interior, closure, [alpha]-closure and [alpha]-interior of A respectively and [G.sub.[alpha]] is the [alpha]-open set for topology [[tau].sub.[alpha]] on X.
The presumption will not apply if the taxpayer "can identify a
subset of elements of dual function computer software that only enables a taxpayer to interact with third parties or to allow third parties to initiate functions or review data (third party
subset)" (REG-153656-03, preamble).
Our investigations relate the Hausdorff measure of a
subset of the Cantor space to the Hausdorff measure of its closure.
Lellis Thivagar [8], introduced the new notion of neutrosophic nano topology, which consist of upper, lower approximation and boundary region of a
subset of a universal set using an equivalence class on it.
In Theorem 14, we shall show that for a
subset F of [C.sub.[phi]] if there exists a closed operator A in H such that T [subset] A for all T [member of] F, then F has a maximal element, and furthermore, if there exists a closed operator B in H such that [([T.sup.-1]).sup.*] [subset] B for all T [member of] F, then F have a maximal element and a minimal element.
Since mR = [[summation].sub.g[member of]A](M) for some
subset A of S,