Abstract
The supremum for a set in a multi-dimensional, Dedikind complete topological space is defined. The example is given to illustrate that the condition of Dedilind complete is necessary for the existence of supremum.
Highlights
We will examine the superemum for a set in a multi-dimensional, Dedikind complete space, which is partially ordered by any pointed, closed and convex cones
There are several types of supremum for a set in multi-dimensional Euclidean space which were introduced by Nieuwenhuis [4], Tanino [3], Zowe [5], Kawasaki [6]
The definition in this paper will be an extension of the regular definition of supremum in Euclidean space to any Dedikind complete topological space
Summary
We will examine the superemum for a set in a multi-dimensional, Dedikind complete space, which is partially ordered by any pointed, closed and convex cones. The definition in this paper will be an extension of the regular definition of supremum in Euclidean space to any Dedikind complete topological space. The relationships among these different kinds of definitions of supremum are examined.
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