A Note on Reordering Ordered Topological Spaces and the Existence of Continuous, Strictly Increasing Functions

Author(s)

Joe Mashburn, University of DaytonFollow

Document Type

Article

Publication Date

1995

Publication Source

Topology Proceedings

Abstract

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 Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rⁿ into R that was strictly increasing with respect to the new order imposed on Rⁿ. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces which have this kind of behavior.

Inclusive pages

207-250

ISBN/ISSN

0146-4124

Document Version

Postprint

Comments

The document available for download is the accepted manuscript, included in the repository with the permission of the publisher. Some differences may exist between this version and the published version; as such, researchers wishing to quote directly from this source are advised to consult the version of record, available online from the publisher.

Permission documentation is on file.

Copyright

Copyright © 1995, Topology Proceedings.

Publisher

Auburn University

Volume

20

Issue

1

Peer Reviewed

yes

eCommons Citation

Mashburn, Joe, "A Note on Reordering Ordered Topological Spaces and the Existence of Continuous, Strictly Increasing Functions" (1995). Mathematics Faculty Publications. 17.
https://ecommons.udayton.edu/mth_fac_pub/17