**Abstract:** Given an X topological space, we will consider the hyperspace of convergent non-trivial sequences, denoted by Sc (X), equipped with the Vietoris topology. We will show some results that relate the connection type properties of said hyperspace with the base space. Later we will give topological results in the context of Baire's spaces. Within this context we will give a characterization of the compaction by a point of a discrete space of unnumbered size. Finally we will extend the Banach-Mazur game to obtain a characterization of the topological spaces whose hyperspace is from Baire. We will mention open problems for future projects.

**Curriculum vitae:** Academic background: Postgraduate studies (PhD): Wesleyan University, E.U.A. Doctor of philosophy June 3, 1990. Postdoctoral studies: University of York, Toronto, Canada. Full-time `` b '' full-time researcher as of October 16, 2002. Fields of expertise: topological groups, forcing, ultrafilter theory, resolvable and irresolvable spaces, pseudocompacity, function spaces, set theory and Euclidean geometry. Scientific production: 90 research articles published in indexed journals, I have 44 co-authors of various nationalities and specialties. Books: Ultrafilters on N and discrete dynamic systems, XXIII Venezuelan School of Mathematics, Editions of the Venezuelan Institute of Scientific Research, Caracas, ISBN 978-980-261-123-2, 2010. digital version of free access; An introduction to the Euclidean geometry of the plane, in process and to be published digitally and freely accessible in the ENES Morelia, ISBN 978-607-30-1013-9, 2019. Academic, professional and scientific distinctions: National Researcher level III, from January 1, 2009 to December 31, 2028. PRIDE level D, from October 1, 2005 to date. Researcher of the State of Michoacán, as of January 1, 2014. Publisher: I am part of the editorial committee of Applied general topology (as of February 24, 2014) and Questions and answers in general topology (as of 16 February 2009). In addition, I have made reviews for Zentralblatt fur mathematik magazine (since 2011) and for Mathematical reviews (since 2016). Creation of congresses: I have been involved in the creation of two international topology congresses in which Mexican topologists have a very important academic participation: Ibero-American Congress of Topology and its Applications and Joint Meeting Japan-Mexico in Topology and its applications (whose name current is Pacific International Conference on Topology and Applications). The reports of these congresses have been published in the magazine Topology and its applications, where I participated as a guest member of the editorial committee of these reports. Conferences: I have lectured in various national and international modalities and forums: 51 research conferences in specialized seminars of various institutions; and 62 research conferences at national and international conferences. Arbitration work: I have carried out arbitration work for specialized journals such as the Bulletin of the Mexican Mathematical Society, Proceedings of the American Mathematical Society, Topology and its Applications, Topology Proceedings, Commentationes Math. Univ. Carolinae, Filomat, etc.