## Fernando Hernández-Hernández

 Facultad de Ciencias Físico Matemáticas Universidad Michoacana de San Nicolás de Hidalgo. Morelia, Michoacán México Tel.: +52 443 322 3500 ext. 1233 Fax: +52 443 326 2146E-mail: fhernandez@fismat.umich.mx
 I have a position at the Facultad de Ciencias Físico Matemáticas in Universidad Michoacana de San Nicolás de Hidalgo. My main research interests are General Topology and Set Theory. Undergraduate: Facultad de Ciencias Físico-Matemáticas at BUAP, Puebla, México.

 A few words about Topology and Set Theory
 General Topology. Topology is a kind of qualitative geometry in which one is interested not in quantitative notions such as the traditional geometry was at its beginnings but in those properties that a "space" posses and that remain after a continuous deformation of it.  Some people has associated the starting point of topology back to the time of Euler and the Königsberg bridge problem. However, it seems to me that defining what means that a given point is in the closure of a given set is the beggining of the true topology going away from geometry. A. V. Arkhange'skii once said that topology is "the science of infinite closeness without distance". I believe that this really describes the essence of topology. Topology is the study of sets on which one has a notion of "closeness" —enough to decide which functions defined on it are continuous. Topology is used in nearly all areas of mathematics in one form or another; so there are many braches of topology. Set-theoretic topology is the branch which studies the most abstract forms of spaces and it is characterized by using wealth of tools from set theory. This is the kind of topology I am interested in. Set Theory. It was initiated by Georg Cantor. The problems about cardinals were the main topic in a first stage of set theory. In that initial period, every "conceivable" set was thought to exists, every collection for which it was possible to say in some way what its elements were was considered a set. It soon turned out that this viewpoint is untenable. The development of axiomatic set theory was then a need. It came the second stage of set theory in which the search for the better axiom system for set theory was the main topic.  Enriched and fortified by axioms, results and techniques axiomatic set theory was launched on its independent course by Gödel in the 1930's.  In the early 1960's set theory was transformed due largely to the creation of forcing by Cohen. According to D. S. Scott "Set theory could never be the same after Cohen, and there is simply no comparison whatsoever in the sophistication of our knowledge about models of set theory today as contrasted to the pre-Cohen era". It is not at all surprising that this development of set theory has a deep impact in topology. Exploring, learning, and taking advantage of it is what moves my interest in set theory.

 Resources
•  A publisher of information related to topology is the Topology Atlas,

• # arXiv.org e-Print archive

• The Mathematics Genealogy Project

• ## (Acrobat Writer 3)

 Publications and Preprints
• Curso de Topología: un enfoque conjuntista. Aportaciones Matemáticas, Serie Textos, Núm. 43. 1st. Edition, 2021. [Extracto PDF]

• Generalized Independence. With Carlos López Callejas. Submitted for publication. [PDF]

• Countable commpact spaces admmitting full r-skeletons are proximal. With Reynaldo Rojas-Hernández. Topology and its Applications 299 (2021). [PDF]

• c-many types of a Ψ-space. With Héctor A. Barriga-Acosta. Topology and its Applications 253 (2019) 1-6. [PDF]

• Topology of Mrówka-Isbell spaces. With Michael Hrušák. In Pseudocompact Topological Spaces, Eds. Hrušák, Tamariz, Tkachenko. Springer International Publishing AG, 2018. [PDF]

• Introducción a Teoría de la Medida. With Manuel Ibarra Contreras. Aportaciones Matemáticas, Serie Textos, Núm. 42. 1a. Edición, 2018. [Extract PDF]

• Non-trivial non weakly pseudocompact spaces. With Reynaldo Rojas-Hernández y Ángel Tamariz-Mascarúa. Topology and its Applications 247 (2018) 1–8. [PDF]

• Scattered spaces from weak diamonds. With Miguel Á. Gaspar-Arreola y Michael Hrušák. Israel Journal of Math 225 (2018) 427-450. [PDF]

• R es único y algo más Aportaciones Matemáticas 1 (2016), Univ. Auto. de Tlaxcala, p. 33-44. [PDF]

• On discretely generated box products. With Héctor A. Barriga-Acosta. Topology and its applications 210 (2016) 1-7. [PDF]

• Dualidad topológica de las álgebras booleanas. With David Meza-Alcántara. Topologí y sus aplicaciones 4. Textos Científicos, BUAP (2016) 81-102. [PDF]

• Árboles y algunas de sus aplicaciones. With David Meza-Alcántara. Topologí y sus aplicaciones 2. Textos Científicos, BUAP (2013) 29-44. [PDF]

• The product of two ordinals is hereditarily dually discrete. With Miguel Á. Gaspar-Arreola. Comment. Math. Univ. Carolin. 53,1 (2012) 99-104. [PDF]

• Conjuntos especiales de números reales. With Alhelí Flores Ferrer, Cecilia Martínez Lázaro, Luis A. Martínez Pérez y Alejandro Torres Ayala. Topologí y sus aplicaciones 1. Textos Científicos, BUAP (2012) 167-186. [PDF]

• Teoría de Conjuntos (una introducción). Undergraduate textbook published in Serie Textos de Aportaciones Matemáticas, Sociedad Matemática Mexicana. Tercera Edición, 2011.

• Martin's Axiom and ω-resolvability of Baire spaces. With Fidel Casarrubias-Segura and Ángel Tamariz-Mascarúa. Comment. Math. Univ. Carolin. 51,3 (2010) 519-540 [PDF]

• Distribuitivity of quotients of countable products of Boolean algebras. Rend. Istit. Mat. Univ. Trieste 41 (2009) 27-34. [PDF]

• A small Dowker space from a club-guessing principle. With Paul J. Szeptycki. Topology Proceedings 34 (2009) 351-363. [PDF]

• When is R the union of an increasing family of null sets? With Juan González-Hernández y César E. Villarreal. Comment. Math. Univ. Carolin. 48,4 (2007) 623-630. [PDF] [DVI] [PS]

• Realcompactness in maximal and submaximal spaces. With Oleg Pavlov, Paul J. Szeptycki y Artur H. Tomita. Topology and its applications 154,16 (2007) 2889-3020. [PDF] [DVI] [PS]

• Pseudocompactness of hyperspaces. With  Michael Hrušák and Ivan Martínez Ruiz.  Topology and its applications 154 (2007) 3048–3055. [PDF] [DVI] [PS]

• Supremum vs. Maximum: $$\lambda$$-sets. Topology and its applications 154,10 (2007) 2081-2088. [PDF] [DVI] [PS]

• A tree π-base for $$\mathbb R^\ast$$ without cofinal branches. Comment. Math. Univ. Carolin. 46 No. 4 (2005) 721-734. [PDF] [DVI] [PS]

• Submodelos elementales en topología. Aportaciones Matemáticas, SMM. Serie Comunicaciones. 35 (2005) 147-174. [PDF] [DVI] [PS]

• Q-sets and normality of Ψ-spaces. With Michael Hrušák. Topology Proceedings 29 No. 1 (2005) 155-165. [PDF] [DVI] [PS]

• Cardinal invariants of analytic P-ideals. With Michael Hrušák. Canadian Journal of Mathematics 59  No.3 (2007) 575-595. [PDF] [DVI]

• Combinatorics of dense subsets of the rationals. With Bohuslav Balcar y Michael Hrušák. Fundamenta Matematicae 183 (2004) 59-80. [PDF]

• A perfectly normal nonrealcompact space consistent with $$MA_{\aleph_1}$$. With Tetsuya Ishiu. Topology and Applications 143 (2004) 175-188.[PDF]

• Teoría de Conjuntos (una introducción). Libro de texto a nivel licenciatura, publicado en Serie Textos de Aportaciones Matemáticas, Sociedad Matemática Mexicana. August 1998 and December 2003 (second edition).

 Links

Last updated Martes Agosto 20, 2013