Some results and examples concerning Whyburn spaces

Ofelia T. Alas, Maira Madriz-Mendoza, Richard G. Wilson


We prove some cardinal inequalities valid in the classes of Whyburn and hereditarily weakly Whyburn spaces and we construct examples of non-Whyburn and non-weakly Whyburn spaces to illustrate that some previously known results cannot be generalized.


Whyburn space; Weakly Whyburn space; Submaximal space; Scattered space; Semiregular; Feebly compact

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A. Bella, C. Costantini and S. Spadaro, The Whyburn property in the class of P-spaces, Quaderni del Dipartimento di Matematica, Universitá de Torino, Quaderno 17/2007.

R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.

I. Juhász, Cardinal Functions in Topology - Ten years later, Mathematisch Centrum, Amsterdam, 1980.

J. Pelant, M. G. Tkachenko, V. V. Tkachuk and R. G. Wilson, Pseudocompact Whyburn spaces need not be Fréchet, Proc. Amer. Math. Soc. 131, no. 10 (2003), 3257–3265.

J. R. Porter and R. G. Woods, Extensions and Absolutes, Springer Verlag, New York, 1987.

E. A. Reznichenko, A pseudocompact space in which only sets of complete cardinality are not closed and not discrete, Moscow Univ. Math. Bull. 6 (1989), 69–70 (in Russian).

V. V. Tkachuk and I. V. Yashchenko, Almost closed sets and the topologies they determine, Comment. Math. Univ. Carolinae 42, no. 2 (2001), 395–405.

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Universitat Politècnica de València

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