... was the same one where I studied. The truth is that we were both a bit embarrassed by this because in addition to being a school run by nuns, we both received very poor pre-university training in mathematics, as we commented on occasion. Later, she was fortunate to study at the National Preparatory School.

... my family thought that my weirdness bordered on extravagance, disorientation and some madness, so they sent me to a psychiatrist.

In a team with other collaborators, Salicrup and Séjourné studied the architecture of Teotihuacán, the enormous city whose remains include the pyramids of the Sun and the Moon, and which forms the archaeological site that is today the most visited in all of Mexico. This city was the home of a civilisation that had its heyday centuries before the Mexica empire - also known as the Aztecs - and of course, before the arrival of the Spanish on the continent. The Aztecs believed that Teotihuacán, which means city of the gods, had been built by giants who still inhabited the earth, hidden from them somewhere.

... to solve something like the inverse problem of discovering the purpose of the different places from their geometry: if this space was a room, if that one was an esplanade, a meeting place, a place for prayer.

If you are convinced of what you want to do, you will always have time.

... was characterised by a close cooperation with her beloved teacher Roberto Vázquez. Graciela and Vázquez were among the first mathematicians who realised that certain topological concepts and constructions were best understood in the light of category theory. ... they analysed topological problems by means of categorical terms and methods, in many cases having first to develop the yet missing categorical machinery. For nearly a decade they produced roughly one joint paper per year, evincing a high sensitivity for suitable problems, and demonstrating great originality and skill. Their best papers of this period ... are prominent achievements in the newly emerging field of categorical topology. Unfortunately they published their results in a journal neither well known nor easily accessible in the non-Spanish speaking mathematical world. Thus, their work which otherwise would have had a considerable impact on categorical topologists - remained for a long time almost unknown, and several of their results had to be recovered independently by later investigators.

Graciela studied a lot: daily, at 8 in the morning, she was already sitting at her desk at the Institute of Mathematics, she prepared her classes impeccably and only when she wanted to give us homework problems did she carry a sheet of paper folded in half. Otherwise, she would arrive to class on time with only her keys in her hand and very seriously enter the room that would later bear her name. She always finished class exactly. Graciela had her routines at the Institute, she waited in her office or went to chat a little with her dear friend María Emilia Caballero. Around eleven o'clock, Graciela would meet with her teacher and collaborator to work. She would leave around two to go to eat.

This book is a version of a three-semester course of topology, which was taught by the author at the National Autonomous University of Mexico City from 1979 to 1980. The author was a well-known specialist in the theory of topological categories and this book is remarkable for its "categorical" spirit. It is separated into three parts, corresponding to three semesters.

Part one contains fundamentals of general topology: pseudometric spaces, bases of topology, maps, products and co-products, axioms of separation, countability axioms, compactness. Part two deals with deeper concepts of general topology and basic notions of homotopic topology: nets, filters, metrizability, convexity, homotopy, fundamental groups, fundamental groups of spheres, function spaces (with the topology of pointwise convergence and with the compact-open topology). Part three is devoted to algebraic topology: covering spaces, fiber spaces, lifting theorem, co-fibrations, adjoint spaces, cell polyhedra. Each part consists of nine sections concluding with several problems.

There were few students and the fact that most of us were mathematicians always made our teachers somewhat nervous; what is true is that Graciela challenged everyone without being aware of it. Here I must point out that she gave us a complex: she was the most attentive, the hardest working, she never boasted of having had previous experience, but on the contrary, she said that she did not remember anything. She always studied, she never failed her homework. Shamelessly just minutes before class we all wanted to be with her so she could help us or, at one point, even shamelessly copy part of her homework.

Tall above average, slender, pretty with an enormous personality, half hidden in that combination that occurs between seriousness and shyness and that, in reality, tries to sift a great intelligence, with a look so tender and so deep at the same time ... Graciela always had her timing well measured. She seemed to have arranged them with the precision of a Swiss watchmaker; she was aware of her family - not just her husband and her children - she regularly visited her mother and helped her with one of her sisters, who needed support. ... Graciela possessed enormous virtues and talents, she had a flair for art, she enjoyed music and she loved opera; she enjoyed painting exhibitions and visiting museums just as much as drawing. Also, she knew a lot about literature and history, she was interested in everything. ... Graciela enjoyed everything, she liked going to the movies - particularly art movies -, several times we went with a group of students, scholarship holders from her Institute and colleagues and classmates from the German class. She accompanied us and we greatly enjoyed her presence. The guided visit to Teotihuacán that she organised with researchers and fellows from the Institute where she worked was famous.

I cannot deny that this situation obviously bothered and saddened Graciela, he was her teacher and her collaborator for years, but perhaps it was very hard for him to see her fly high, with her own wings and with her own creativity and originality. I insist, this is imagination but I say this because I know Graciela always felt respect for Dr Vázquez.

Some of the relationships among the topological notions: 'Hausdorff', 'compact', 'perfect', and 'closed' are abstracted to a more general categorical setting, where they are shown to remain intact. An investigation is made of factorization structures (especially for single morphisms) and their relationships to strong limit operators and to the Pumplün-Röhrl Galois correspondence between classes of objects and classes of morphisms in any category. Many examples as well as internal characterisations of Galois-closed classes are provided.

Many of the ideas and results included in this paper are due to the second author [Graciela Salicrup], and were incorporated in an unfinished manuscript that she was preparing shortly before her untimely death in 1982.

Five years have passed since Graciela died. Her life was untimely interrupted by a fatal accident. We lost a friend, Mexico lost a gem. Mexico is a very young country. Even younger is his mathematical tradition. Mathematical activity is twice as difficult if there is no tradition backing it. This doubles the merits of Graciela: she not only was a pioneer in a newly created branch of mathematics, she consciously helped to build up a tradition in a country where mathematical research goes back just to the end of the thirties and now is scarcely fifty years old. Being a woman, her task was particularly difficult. We miss the lovely person, who was always there to listen to our problems and to give sound advice. She was a fair judge and her opinion was as important for moderating as for animating. We miss the mathematician, from whom many of us learned so much, whose lectures were always clear, thoroughly prepared and inspiring, and who knew how to explain well the importance of precision and mathematical rigour. ... We hope that this compilation helps to do justice to the scientific work of an inspired mathematician. Graciela lives in her mathematical work, she lives in her archaeological investigations. Graciela lives in our hearts.