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Lindelöf Σ-spaces: an omnipresent class

Espacios Lindelöf Σ: una clase ubicua

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

This survey’s first object is to introduce the reader to Lindelöf Σ-spaces; since the author would like this introduction to be useful for postgraduate students and non-specialists in the area, most of the basic results are given with complete proofs.

The second object is to make an overview of the recent progress achieved in the study of Lindelöf Σ-spaces. Several popular topics are presented together with open problems, some old and some new. The main idea is to show the areas of major activities displaying what is being done nowadays and trying to outline the trends of their future development. A big percentage of the cited results and problems are new, i.e., published/obtained in the 21-st century. However, some classical old theorems and questions are also discussed the author being convinced that they are worth to be repeated with a new emphasis due to the modern vision of the area.

Resumen

El primer objetivo de este artículo es brindar una introducción a la teoría de los espacios Lindelöf Σ; el autor quisiera que dicha introducción fuera útil tanto para los estudiantes de posgrado como para los que no son especialistas en el área, así que la mayoría de los resultados básicos se presentan con demostraciones completas.

El segundo objetivo es describir, a grandes rasgos, los avances modernos en el estudio de los espacios Lindelöf Σ. Al respecto presentamos algunos temas populares, tanto recientes como ya establecidos desde hace tiempo. La idea principal es mostrar las áreas de mayor actividad, esbozando lo que se está haciendo hoy en día y tratando de visualizar las tendencias para el futuro desarrollo de dichas áreas. Un porcentaje considerable de los resultados citados son nuevos, es decir, obtenidos en el siglo 21. Sin embargo, presentamos también bastantes teoremas clásicos y preguntas abiertas viejas ya que el autor está convencido de que merecen ser mencionados con un nuevo énfasis debido a la visión moderna del área.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, A.P. 55-532, C.P. 09340, Iztapalapa, México, D. F.

    Vladimir V. Tkachuk

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Correspondence to Vladimir V. Tkachuk.

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Dedicated to professor Manuel Valdivia on the occasion of his 80th birthday

Submitted by José Bonet

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Tkachuk, V.V. Lindelöf Σ-spaces: an omnipresent class. RACSAM 104, 221–244 (2010). https://doi.org/10.5052/RACSAM.2010.15

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