Compact Hausdorff group topologies for the additive group of real numbers

This volume contains the contributions presented by several colleagues as a tribute to the mathematical and human qualities of Jos e Mar a Montesinos Amilibia on the occasion of his seventieth birthday. The editors would like to express their thanks to the contributors and their very especial gratitude to Jos e Mar a for his example through many years of scienti c and personal contactWe deal with an example of a topology for the additive group of real numbers R, which makes it a compact Hausdor topological group. Further, (R; ) is connected, but neither arcwise connected, nor locally connected. Thus, it is nei- ther a Lie group, nor a curve in the sense of H. Mazurkiewicz. The contribution of this short note is to provide an elementary proof of the fact that it is not arcwise connected.Peer ReviewedPostprint (published version

Pontryagin duality in the class of precompact Abelian groups and the Baire property

We present a wide class of reflexive, precompact, non-compact, Abelian topological groups G determined by three requirements. They must have the Baire property, satisfy the open refinement condition, and contain no infinite compact subsets. This combination of properties guarantees that all compact subsets of the dual group G∧ are finite. We also show that many (non-reflexive) precompact Abelian groups are quotients of reflexive precompact Abelian groups. This includes all precompact almost metrizable groups with the Baire property and their products. Finally, given a compact Abelian group G of weight ≥ 2!, we find proper dense subgroups H1 and H2 of G such that H1 is reflexive and pseudocompact, while H2 is non-reflexive and almost metrizable.Peer ReviewedPreprin

Strong reflexivity of Abelian groups

A reflexive topological group G is called strongly reflexive if each closed sub-group and each Hausdorff quotient of the group G and of its dual group is reflexive. In this paper we establish the adequate concept of strong reflexivity for convergence groups and we prove that the product of countable many locally compact topological groups and complete metrizable nuclear groups are BB-strongly reflexive

EngiMath online course. Effective feedback from upc mathematics teachers (concept)

EngiMath is a 3 ECTS online course in engineering mathematics, in seven different languages, and it is the main and practical output of the ERASMUS+ project entitled “Mathematics online learning model in engineering education” in which the authors were participating. The course is integrated with Learning Management Systems such as Moodle and it is compatible with other platforms using Learning Tools Interoperability. Once the project is finished, authors undertake, with the support of the Institute of Education Sciences at the Universitat Politècnica de Catalunya-BarcelonaTECH (UPC), an innovation project, EngiMath@UPC, with three practical objectives: a) to incorporate EngiMath into the teaching activity of the widest as possible range of students at UPC, b) to gather students and faculty feedback regarding the tracking of materials and their performance in the student training process, and c) to statistically analyze the data collected in order to validate and adjust the follow-up of the materials. In connection with the above mentioned objective b) a training course addressed to the math professors has been prepared at UPC. The paper introduces, on the one hand, the EngiMath course as an online open educational resource for the academic community benefit, and on the other hand, analyzes the valuable feedback given by the training activity participants. Details on the online course implementation as well as main conclusions will be presented and discussed throughout the document

Completeness properties of locally quasi-convex groups

It is natural to extend the Grothendieck Theorem on completeness, valid for locally convex topological vector spaces, to abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, in this paper we present examples of metrizable locally quasi-convex groups for which the analogue to Grothendieck Theorem does not hold. By means of the continuous convergence structure on the dual of a topological group, we also state some weaker forms of Grothendieck Theorem valid for the class of locally quasi-convex groups. Finally, we prove that for the smaller class of nuclear groups, BB-reflexivity is equivalent to completeness

Online engineering mathematics course : development and implementation of a successful project

According to the New UNESCO global survey studying the effect of Covid-19 on higher education (2021) the pandemic has had an impact on higher education systems in terms of access and quality of teaching and learning. Covid-19 has caused the suspension and cancellation of teaching activities and its major impact on teaching and learning is the increase in online education. The Engimath - Mathematics on-line learning model in engineering education - was successfully carried out at the very right moment, as in recent two years there has been a significant increase in demand for a 100% online mathematics course with interactive learning materials and largescale practicing opportunities as well as for a mathematics online assessment model. This project has successfully developed a high-level online course as a basis for offering output-oriented education in engineering mathematics. Some of development stages, that led this project – EngiMath - to an outstanding successful end, will be presented in this paper. These go from the educational needs’ analysis to its implementation and use, even allowing an open and live test.Peer ReviewedObjectius de Desenvolupament Sostenible::4 - Educació de QualitatObjectius de Desenvolupament Sostenible::4 - Educació de Qualitat::4.3 - Per a 2030, assegurar l’accés en condicions d’igualtat per a tots els homes i dones a una formació tècnica, professional i superior de qualitat, inclòs l’ensenyament universitariObjectius de Desenvolupament Sostenible::4 - Educació de Qualitat::4.4 - Per a 2030, augmentar substancialment el nombre de joves i persones adultes que tenen les competències necessàries, en particular tècniques i professionals, per a accedir a l’ocupació, el treball digne i l’emprenedoriaPostprint (published version

MÈTODES MATEMÀTICS I (Examen 1er. quadrim. )

Pràctica puntuable d'Àlgebra(5% nota

MÈTODES MATEMÀTICS I (Examen 1er. quadrim. )

Examen Problemes (50% nota

MÈTODES MATEMÀTICS I (Examen 1er. quadrim. )

Test d'Àlgebra (20% nota

MÈTODES MATEMÀTICS I (Examen 1er. quadrim. )

Pràctica puntuable de Càlcul(5% nota