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  • https://math.libretexts.org/Bookshelves/Analysis/Mathematical_Analysis_(Zakon)/04%3A_Function_Limits_and_Continuity/4.07%3A_More_on_Compactness
    If {Gi} is an open covering of F, then each point xF 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 xF 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 xF. If, however, they can be chosen all equal to some ε, then this ε is called a…

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