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

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**Last modified March 16, 2001.**