Electronic Version 20 (1995), 207-250

J. D. Mashburn

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with \Bbb Rⁿ and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from \Bbb Rⁿ into \Bbb R that was strictly increasing with respect to the new order imposed on \Bbb Rⁿ. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces which have this kind of behavior.

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volume 20: table of contents
topology proceedings Electronic Version