If {Gi} is an open covering of F, then each point x∈F is in some Gi and is its interior point ( for Gi is open ), so there is...If {Gi} is an open covering of F, then each point x∈F is in some Gi and is its interior point ( for Gi is open ), so there is a globe Gx(εx)⊆Gi. In general, the radii εx of these globes depend on x, i.e., are different for different points x∈F. If, however, they can be chosen all equal to some ε, then this ε is called a…