Generic theorems in the theory of cardinal invariants of topological spaces

Alejandro Ramírez-Páramo; Jesús F. Tenorio

doi:10.4995/agt.2019.10682

Authors

Alejandro Ramírez-Páramo Benemérita Universidad Autónoma de Puebla
Jesús F. Tenorio Universidad Tecnológica de la Mixteca https://orcid.org/0000-0003-0705-3394

DOI:

https://doi.org/10.4995/agt.2019.10682

Keywords:

cardinal functions, compact spaces, Lindelöf spaces, weak Hausdorff number of a space

Abstract

The main aim of this paper is to present a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related. Moreover, we use this result and the weak Hausdorff number, H^âˆ—, introduced by Bonanzinga in [Houston J. Math. 39 (3) (2013), 1013–1030], to generalize some upper bounds on the cardinality of topological spaces.

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Author Biographies

Alejandro Ramírez-Páramo, Benemérita Universidad Autónoma de Puebla

Facultad de Ciencias de la Electrónica

Jesús F. Tenorio, Universidad Tecnológica de la Mixteca

Instituto de Física y Matemáticas

References

O. T. Alas, More topological cardinal inequalities, Colloq. Math. 65, no. 2 (1993), 165-168. https://doi.org/10.4064/cm-65-2-165-168

A. V. Arhangel'skii, A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carolin. 36, no. 2 (1995), 303-325.

A. V. Arhangel'skii, The power of bicompacta with first axiom of countability, Sov. Math. Dokl. 10 (1969), 951-955.

A. Bella, On two cardinal inequalities involving free sequences, Topology Appl. 159 (2012), 3640-3643. https://doi.org/10.1016/j.topol.2012.09.008

M. Bonanzinga, D. Stavrova and P. Staynova, Separation and cardinality - Some new results and old questions, Topology Appl. 221 (2017), 556-569. https://doi.org/10.1016/j.topol.2017.02.007

M. Bonanzinga, On the Hausdorff number of a topological space, Houston J. Math. 39, no. 3 (2013), 1013-1030.

F. Cammaroto, A. Catalioto and J. Porter, On the cardinality of Hausdorff spaces, Topology Appl. 160 (2013), 137-142. https://doi.org/10.1016/j.topol.2012.10.007

F. Cammaroto, A. Catalioto and J. Porter, On the cardinality of Urysohn spaces,

A. Charlesworth, On the cardinality of a topological space, Proc. Amer. Math. Soc. 66, no. 1 (1977), 138-142. https://doi.org/10.1090/S0002-9939-1977-0451184-8

A. A. Gryzlov, Two theorems on the cardinality of topological spaces, Soviet Math. Dokl. 21 (1980), 506-509.

R. E. Hodel, A technique for proving inequalities in cardinal functions, Topology Proc. 4 (1979), 115-120.

R. E. Hodel, Arhangel'skii's solution to Alexandroff's problem: A survey, Topology Appl. 153, no. 13 (2006), 2199-2217. https://doi.org/10.1016/j.topol.2005.04.011

R. E. Hodel, Cardinal functions I, in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 1-61. https://doi.org/10.1016/B978-0-444-86580-9.50004-5

I. Juhász, Cardinal functions in topology- 10 years later, Math. Center Tract. 123, Amsterdam, 1980.

S. Shu-Hao, Two new topological cardinal inequalities, Proc. Amer. Math. Soc. 104 (1988), 313-316. https://doi.org/10.2307/2047509

S. Spadaro, A short proof of a theorem of Juhász, Topology Appl. 158, no. 16 (2011), 2091-2093. https://doi.org/10.1016/j.topol.2011.06.002

S. Willard and U. N. B. Dissanayake, The almost Lindelöf degree, Canad. Math. Bull. 27, no. 4 (1984), 452-455. https://doi.org/10.4153/CMB-1984-070-2