Gilberto Francisco Loibel was the son of Franz Loibel and Gertrudes Loibel Reyar, German chemical engineers who came to São Paulo in 1929, during the crisis in Europe. His only sister, Angelica, was born in Germany a few years earlier. The family returned to Germany in 1939, shortly before the outbreak of World War II, which took place in September of the same year. The family returned to Brazil in 1947.

... born in Italy, and arrived in Brazil in 1939 at the invitation of the Brazilian government to teach at the National Faculty of Philosophy, part of the University of Brazil, located in Rio de Janeiro. He went through other Brazilian educational institutions until, in 1953, he received an invitation to organise the Department of Mathematics at the School of Engineering of São Carlos, University of São Paulo. In this institution, he also taught, and supervised undergraduate and graduate students ...

The organisation of the Department of Mathematics was under the responsibility of Professor Achille Bassi, who endeavoured to acquire a bibliographic collection and hire qualified researchers to form a research centre in Mathematics. In this way, the Department was created with post-graduate courses. Professor Achille Bassi's determination to create an excellent library gave rise to one of the best libraries in the country in the area of Mathematics ... The Department of Mathematics was then formed by professors Achille Bassi, Jauréz Cecconi and Ubaldo Richard and some engineers who came from the Polytechnic School on a part-time basis ... Professor Jaurez Cecconi was an analyst. His research papers on Calculus of Variations and Optimisation were published between 1951 and 1985, mainly in Italian journals. Professor Ubaldo Richard was also an analyst. His research papers on Differential Equations and Integral Equations were published between 1940 and 1982, mainly in Italian journals.

This paper constitutes the first three of the four chapters of the author's doctoral thesis. The first of these is an exposition of well-known results in (algebraic) quasi-groups ... A quasi-group with a multiplicative identity is a loop. The remaining two chapters are devoted to a development of certain fundamental notions, adaptations from topological groups, for topological quasi-groups. A topological quasi-group [loop] is a quasi-group [loop] endowed with a topology under which its operations are continuous; or what amounts to the same thing, a topological space which admits a compatible quasi-group [loop] structure. ... The main theorems of the second chapter include (1) the observation that a topological space which admits a quasi-group structure also admits a loop structure, (2) a characterisation of the notion of a fundamental system of neighbourhoods of the identity of a Hausdorff loop, (3) a homomorphism theorem for topological loops, and (4) a necessary condition for two topological loops to be locally isomorphic.

The author studies continuous multiplications with identity defined on a Cartesian product of spheres. He determines when such multiplications exist; when they exist, he classifies them in terms of homotopy groups of spheres. He then states, for example, that a homotopy-commutative product can exist only on a product of circles.

The systems mentioned in the title are topological spaces with a continuous multiplication with left unit such that the equation xa = b is continuously uniquely solvable for x. Some general (and, on the whole, superficial) features of topological group theory carry over to these structures, e.g., the standard statements about substructures, continuous and open homomorphisms, separation properties, and connectivity. (For example, the closure of a subsystem is a subsystem. Open subsystems are closed. Connected systems are generated by each neighbourhood of the left unit, etc.) A useful observation (even in the case of groups) is this: If a system S is such that every 1-1 continuous map of $S \times S$ onto itself is a homeomorphism, then the continuity of multiplication implies the continuity of the solution, and conversely (the condition is satisfied if S is compact or is a manifold). A general notion of uniformity is introduced to fit the purpose of invariantly uniformising a system. Most of the results in the theory of covering structures are flexible enough to hold for the systems considered. However, an example is given of a system on the 2-torus which is covered by a system on the plane but is not covered by any system on the cylinder.

... we were suffocated inside the São Carlos School of Engineering, obviously because the important thing was engineering. Mathematics and numerical analysis were in the background, they were suffocated inside. The issue was not only related to funding for staff and laboratories, but also for the library.

Together with a small group of pioneering professors, Loibel played a fundamental role in the creation and consolidation of the then Institute of Mathematical Sciences of São Carlos.

According to Gilberto Francisco Loibel, at that time there were groups of professors who sympathised with various different positions regarding the creation of an Institute. Some of them, including Professor Loibel, defended the idea of bringing together the Basic Sciences in a single Institute separate from the Engineering School. However, this was not the position that the head of the Mathematics Department defended, as he was thinking of creating an Institute solely for his area.

... in addition to being the person who introduced the Theory of Singularities in Brazil, Loibel was the founder of the Grupo de Singularidades de São Carlos. He supervised the first master's and doctoral students in this area, mainly from 1970 to 1985. Many of the dissertations and theses supervised by Loibel were pioneers in the topics covered, thanks to the supervisor's brilliance. He was one of the most brilliant mathematicians I ever met ...

The sum of the couple's experience, is a career of seventy years. Gilberto even presided over the founding meeting of the Brazilian Society of Mathematics, in 1969, and is a founding member of the Academy of Sciences of the State of São Paulo. The two were part of the construction process for research in the city of São Carlos, in the interior of São Paulo. "In addition to promoting and encouraging academic activity in Coxim, the colloquium aims to share the experience of the two speakers on how to create an academic culture for a city," emphasises Professor Tadeu Cândido, coordinator of the event.

The Institute of Mathematics and Computer Sciences (ICMC) of the University of São Paulo, in São Carlos, inaugurated the Professor Loibel hyperspace on 20 November 2014, located in the opening of the Achille Bassi Library. The tribute took place one year after the death of Professor Gilberto Francisco Loibel, one of the main drivers of the study and research environment in mathematics in the interior of the State of São Paulo.