Extending connectivity functions on Rn


Krzysztof Ciesielski, Tomasz Natkaniec, Jerzy Wojciechowski

Topology Appl. 112(2) (2001), 193-204.

A function f:Rn-->R is a connectivity function if for every connected subset C of Rn the graph of the restriction f|C is a connected subset of Rn+1, and f is an extendable connectivity function if f can be extended to a connectivity function g:Rn+1-->R with Rn embedded into Rn+1 as Rnx{0}. There exists a connectivity function f:R-->R that is not extendable. We prove that for n>1 every connectivity function f:Rn-->R is extendable.

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Last modified March 16, 2001.