Abstract
A space is connected if it is not the union of two disjoint non-empty closed sets. An equivalent condition is that there does not exist a continuous mapping of the space onto the discrete space having two points. From the latter condition it is easy to see that a space X is connected if and only if βX is connected.
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© 1974 Springer-Verlag Berlin Heidelberg New York
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Walker, R.C. (1974). Local Connectedness, Continua, and X*. In: Walker, R.C. (eds) The Stone-Čech Compactification. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61935-9_9
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DOI: https://doi.org/10.1007/978-3-642-61935-9_9
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