Strongly pseudocompact topological groups

• Grant number: 16/23440-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: January 31, 2017
• End date: February 17, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Artur Hideyuki Tomita
• Grantee: Artur Hideyuki Tomita
• Visiting researcher: Salvador Garcia Ferreira
• Visiting researcher institution: Universidad Nacional Autónoma de México, Morelia (UNAM), Mexico
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The notion of strongly pseudocompact space was introduced in [1]. In the paper [2], a pseudocomapct group which is not strongly pseudocompact is constructed. This makes very interesting to study the strongly pseudocompact topological groups and the strongly pseudocompact homogeneous spaces. A countably compact space whose square is not pseudocompact shows that strong pseudocompactness is not productive in the class of spaces (see [3]). This makes natural to ask what about topological groups and homogeneous spaces. The proposed project will addresses this problem. Also we shall try to solve some open questions, in the context of topological groups, of a recent results of D. Shakmatov and A. Dorantes. We conjecture that adding some axiom to the system of ZFC we can construct two strongly compact groups whose product is not strongly pseudocompact. [1] S. Garcia-Ferreira, Y. F. Ortiz-Castillo, Strong pseudocompact properties, Comment. Math. Univ. Carolin. 55, 1, 2014, 101-109. [2] A pseudocompact group which is not strongly pseudocompact, S. Garcia-Ferreira y A. H. Tomita. Topology Appl. 192 (2015), 138-144. [3] Gillman L., M. Jerison, Rings of Continuous Functions, Springer Verlag, Graduate Tex.s in Math., N.Y., Heidelberg, Berlin, 1976. (AU)