Artículo Original
Publicado 2018-12-12
Palabras clave
- Función cardinal,
- grupo topológico,
- índice de acotamiento
Cómo citar
Ramírez-Páramo, A., & Tenorio, J. F. (2018). Sobre el índice de acotamiento de grupos topológicos. Revista Integración, Temas De matemáticas, 36(2), 83–99. https://doi.org/10.18273/revint.v36n2-2018002
Resumen
Estas notas proporcionan una breve introducción al índice de acotamiento en grupos topológicos. Damos, de manera casi autosuficiente, las herramientas necesarias de funciones cardinales, así como los hechos básicos de la teoría de grupos topológicos.
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Referencias
[1] Alexandroff P. and Urysohn P., “Mémoire sur les éspaces topologiques compacts”, Ver. Akad. Wetensch, Amsterdam 14 (1929), 1–96.
[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.
[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.