Semilinear (Topological) Spaces and Applications : June, 1971 (Classic Reprint)

Excerpt from Semilinear (Topological) Spaces and Applications: June, 1971

In this paper we define semivector spaces and develop some of their algebraic aspects including some structure theory; then top 0pogize these spaces to obtain semilinear topological spaces for which we identify a hierarchy of local convexity axioms; establish a number of fixed point and minmax theorems for spaces with various local convexity properties; illustrate how the spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces; and, finally, indicate briefly how all the above are applied in socio-economic analysis and optimization.

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