Research and Innovation Articles
Published 2018-12-12
Keywords
- Cardinal function,
- topological group,
- index of boundedness
How to Cite
Ramírez-Páramo, A., & Tenorio, J. F. (2018). On the index of boundedness of topological groups. Revista Integración, Temas De matemáticas, 36(2), 83–99. https://doi.org/10.18273/revint.v36n2-2018002
Abstract
These notes provide a brief introduction to the index of boundedness in topological groups. We give, in an almost self-contained way, the necessary tools of cardinal functions, as well as the basic facts of the theory of topological groups.
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References
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[11] TkachenkoM.G., “Cellularity and the index of narrowness in topological groups”, Comment. Math. Univ. Carolin. 52 (2011), No. 2, 309–315.
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[13] Tkachenko M.G., “Paratopological and Semitopological Groups Versus Topological Groups”, In Recent Progress in General Topology III (2014), 825–882.
[14] Tkachenko M.G., “Topological features of topological groups”, In Handbook of the History of General Topology Vol 3 (2001), 1027–1144.
[15] Tkachenko M.G., Villegas Silva L.M., Hernández García C. y Rendón Gómez O.J., Grupos topológicos, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Primera edición 1997.
[16] Torres Falcón Y., “Unions of chains of subgroups of a topological group”, Appl. Gen. Topol. 2 (2001), No. 2, 227–235.
[2] Arhangel’skii A.V. and Tkachenko M., Topological groups and related structures, Atlantis Studies in Mathematics, Atlantis Press, 2008.
[3] Bell M., Ginsburg J. and Woods G., “Cardinal inequalities for topological spaces involving the weak Lindelöf number”, Pacific J. Math. 79 (1978), No. 1, 37–45.
[4] Casarrubias-Segura F. and Ramírez-Páramo A., “Some reflection theorems”, Topology Proc. 31 (2007), No. 1, 51–65.
[5] Charlesworth A., “On the cardinality of a topological space”, Proc. Amer. Math. Soc. 66 (1997), No. 1, 138–142.
[6] Engelking R., General topology, Translated from the Polish by the author, 2nd ed. Sigma Series in Pure Mathematics, Vol 6, Heldermann Verlag, Berlin, 1989.
[7] Hodel R.E., “Arhangel’skiˇı’s solution to Alexandroff’s problem: A survey”, Topology Appl. 153 (2006), No. 13, 2199–2217.
[8] Hodel R.E., “Cardinal functions I”, In Handbook of set-theoretic topology, Edited by K. Kunen and J. E. Vaughan, North-Holland, Amsterdam (1984), 1–61.
[9] Hodel R.E. and Vaughan J.E., “Reflection theorems for cardinal functions”, Topology Appl. 100 (2000), 47–66.
[10] Juhász I., Cardinal functions in topology-10 years later, Math. Center Tract. 123, Amsterdam, 1980.
[11] TkachenkoM.G., “Cellularity and the index of narrowness in topological groups”, Comment. Math. Univ. Carolin. 52 (2011), No. 2, 309–315.
[12] Tkachenko M.G., “Introduction to topological groups”, Topology Appl. 86 (1998), 179–231.
[13] Tkachenko M.G., “Paratopological and Semitopological Groups Versus Topological Groups”, In Recent Progress in General Topology III (2014), 825–882.
[14] Tkachenko M.G., “Topological features of topological groups”, In Handbook of the History of General Topology Vol 3 (2001), 1027–1144.
[15] Tkachenko M.G., Villegas Silva L.M., Hernández García C. y Rendón Gómez O.J., Grupos topológicos, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Primera edición 1997.
[16] Torres Falcón Y., “Unions of chains of subgroups of a topological group”, Appl. Gen. Topol. 2 (2001), No. 2, 227–235.