Abstract
a) If A contains the range of the net n converging to a then for each for each N (a), n is eventually in N(a) whence N(a) ∩A ≠ ø and so a ∈ Ā. If Λ is the diset N(a) then the range of the net n : Λ ∋ N ↦ n(N) ∈ N ∩ A is contained in A and n converges to a
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© 1992 Springer Science+Business Media New York
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Gelbaum, B.R. (1992). Topology, Limits, and Continuity. In: Problems in Real and Complex Analysis. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0925-6_17
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DOI: https://doi.org/10.1007/978-1-4612-0925-6_17
Publisher Name: Springer, New York, NY
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