Some results and examples concerning Whyburn spaces

Ofelia T. Alas

Brazil

Universidade de Sao Paulo

Instituto de Matemática e Estatística, Universidade de Sao Paulo, Caixa Postal 66281, 05311-970 Sao Paulo, Brasil

Maira Madriz-Mendoza

Mexico

Universidad Autónoma Metropolitana

Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco, #186, Apartado Postal 55-532, 09340, México, D.F., México

Richard G. Wilson

Mexico

Universidad Autónoma Metropolitana

Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco, #186, Apartado Postal 55-532, 09340, México, D.F., México

Submitted: 2013-07-29

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Accepted: 2013-07-29

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Published: 2012-04-15

DOI: https://doi.org/10.4995/agt.2012.1633
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Keywords:

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

Supporting agencies:

This research was supported by the network Algebra

Topología y Análisis del PROMEP

Project 12611243 (México) and Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo (Brasil).

Abstract:

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.
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References:

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. http://dx.doi.org/10.1090/S0002-9939-02-06840-5

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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