COMPACT SETS OF FUNCTIONS AND FUNCTION RINGS

@inproceedings{Gale2010COMPACTSO,
  title={COMPACT SETS OF FUNCTIONS AND FUNCTION RINGS},
  author={David Gale},
  year={2010}
}
A widely used theorem of analysis asserts that a uniformly bounded, equicontinuous family of functions has a compact closure in the space of continuous functions. This lemma, variously attributed to Arzela, Escoli, Montel, Vitali, and so on, is of importance in the theory of integral equations, conformal mapping, calculus of variations, and so on. In recent years the lemma has been generalized by S. B. Myers [l].1 A part of his results may be formulated as follows; If a topological space X is… CONTINUE READING

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