Extending Connectivity Functions on R
نویسندگان
چکیده
A function f : R → R is a connectivity function if for every connected subset C of R the graph of the restriction f |C is a connected subset of R, and f is an extendable connectivity function if f can be extended to a connectivity function g : R → R with R imbedded into R as R × {0}. There exists a connectivity function f : R → R that is not extendable. We prove that for n ≥ 2 every connectivity function f : R → R is extendable.
منابع مشابه
Extending connectivity functions on R n ✩
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 Rn × {0}. There exists a connectivity function f :R→ R that is not extendable. We prove that for n 2 every connec...
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