If f is a contraction from a complete modified semi-linear uniform space X to X, is f has a unique fixed point?

Abdalla Ahmad Tallafha @Abdalla-Tallafha

09 August 2017 0 8K Report

We shall call a semi-linear uniform space (X,Γ) a modified semi-linear uniform space, if Γ satisfies the following additional conditions.

1- For all V∈Γ,we have union nV=X×X.

2- δ(x,y)⊆δ(x,z)∘δ(z,y) for all x,y and z∈X.

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