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François G. Dorais
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Yes, see for example "Continua which admit only the identity mapping onto non-degenerate subcontinua""Continua which admit only the identity mapping onto non-degenerate subcontinua" by H. Cook (Fund. Math. 60, 1967, 241-249).

Yes, see for example "Continua which admit only the identity mapping onto non-degenerate subcontinua" by H. Cook (Fund. Math., 1967).

Yes, see for example "Continua which admit only the identity mapping onto non-degenerate subcontinua" by H. Cook (Fund. Math. 60, 1967, 241-249).

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Ramiro de la Vega
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Yes, see for example "Continua which admit only the identity mapping onto non-degenerate subcontinua" by H. Cook (Fund. Math., 1967).