The Spiral

Abstract: We call The Spiral the simplest compactification of the ray [0,1) with remainder the unit circle S in the plane. From the point of view of Continuum Theory, one might think that this spiral does not have much significance. In this talk we refute this impression, as we will see that it has a relevant role in several topics: uncoherent in products and symmetric products, the fixed point theory, colocal connectedness, coselections, hyperspaces homeomorphic to cones, etc.

Semblance: Researcher C at the UNAM Mathematics Institute. He has published 166 research articles between 1985 and 2025, also 5 books, one of which whit international circulation, (Marcel Dekker, Hyperspaces, with Sam B. Nadler, Jr., 1999). And the most recent of these is Continuum Theory, edited by Springer. He has directed 32 bachelor's theses, 6 master's theses, and 16 doctoral theses. More than 90 research talks at international meetings, with 13 plenary sessions. A large number of dissemination talks and talks, at colloquia in 16 universities. Reviewer for more than 20 research journals, also books, projects, dissemination articles, etc. Commentator for Mathematical Reviews and Zentralblatt MATH. Professor at UNAM since April 1978, he has taught more than 100 courses. He has worked at CIMAT in Guanajuato (1992), California State University in Sacramento (2004) and Texas Tech University in Lubbock, Texas (Aug. 2013-Jul. 2014). Member of the SNII since 1986, with level III since 2000 and emeritus since 2021. He worked for the Mexican Mathematical Olympiad as an organizer, head of delegation, giving mini-courses to teachers, coach, book editor, co-author of brochures and author of a book, etc.

• Winner of the “National University Distinction for Young Academics” in exact sciences, teaching, UNAM, November 1994.
• Winner of the “UNAM Award” in exact sciences, teaching, November, 2005.
• Head of the Jury of the International Mathematical Olympiad, Mérida, Yucatán, 2005.

For Conacyt, he worked on the SNI Evaluation Committee (2015-2017), the Basic Science Projects Evaluation Committee and the Patrimonial Chairs Evaluation Committee.