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Extending Connectivity Functions on Rn
by
Jerzy Wojciechowski
West Virginia University
Coauthors: Krzysztof Ciesielski, Tomasz Natkaniec
A function f from Rn to R is a connectivity function if for every connected subset C of Rn the graph of the restriction of f to C is a connected subset of Rn+1, and f is an extendable connectivity function if there exists a connectivity function g from Rn+1 to R that extends f, with Rn imbedded into Rn+1 as Rnx0. It folows immediately from the definition that every extendable connectivity function is a connectivity function. There exists a connectivity function from R to R that is not extendable. We prove that for n > 1 every connectivity function from Rn to R is extendable.
Date received: February 11, 1998
Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caas-56.