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Lemma 1

[2FY]If \(Y⊆ X\) is connected and \(Y⊆ E ⊆ \overline Y\), then \(E\) is connected.

For the proof, See Teorema 5.11.6 in [ 3 ] , or Theorem 20 in Cap. 1 in [ 15 ] .

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Authors: "Mennucci , Andrea C. G." .

Bibliography

[3] L. Ambrosio, C. Mantegazza, and F. Ricci. Complementi di matematica. Scuola Normale Superiore, 2021. ISBN 9788876426933. URL https://books.google.it/books?id=1QR0zgEACAAJ.
[17] J.L. Kelley. General Topology. Graduate Texts in Mathematics. Springer New York, 1975. ISBN 9780387901251. URL https://books.google.it/books?id=-goleb9Ov3oC.

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