Fico became interested in this problem after reading an article by the eminent British mathematician J H C Whitehead, where he proves the theorem under very restrictive assumptions. Fico's result is still little known as it was written in Spanish and in a small-circulation magazine that disappeared more than 40 years ago. However, it is so deep and important that over the years articles with partial proofs have continued to appear, and even other articles where it is stated, erroneously, that the result is false in general.

We prove that, for any topological space X and any metric space (Y, d), the fine topology on the space of continuous functions from X into Y is independent of the metric d.

I wish to express my deep gratitude to my adviser, Professor Ralph H Fox, to whom, for his valuable orientation, help and advice, I owe the completion of this thesis. I want to thank Dennis Sullivan for introducing $H^{3}$ to me. For very helpful conversations and explanations I wish to thank Professors W Browder, W Massey and C D Papakyriakopoulos, as well as S Lopez de Medrano, M O'Nan and E Winkelnkemper. I also would like to express my indebtedness to Professors Solomon Lefschetz, José Adem and Roberto Vázquez García.

I have received financial support from the UNAM, the Institute Nacional de la Investigacion Cientifica and Princeton University.

Last but not least, I want to thank my wife Susana for typing the thesis and for her constant encouragement.

In his thesis Fico studies a type of differentiable varieties known as "homological spheres", whose study is of the utmost importance and stems from the famous "Poincaré Conjecture". Fico's thesis contains such a quantity of quality results that we can well say that it contains enough material for two very good theses. In the first part he studies cobordism groups of smooth homological n-spheres, and proves that for dimensions other than 3, such a group is isomorphic to the group of smooth homotopic spheres defined by Kervaire and Milnor. He also considers the cobordism group of homologous n-spheres embedded in a m-sphere, and proves that for dimensions other than 3 and 4, it is isomorphic to the group of pairs of homotopic n-spheres embedded in a m-sphere, defined by Levine. To do all this one needs to have extensive knowledge of the differential topology of higher-dimensional manifolds. For the case n = 3, this group is still unknown, but in the second part of his thesis Fico studies the homological 3-spheres obtained by Dehn's surgery in knots. ...

I have looked at your paper and you have a lovely and important result. I recommend that you aim very high where you send the paper. I would try the 'Annals of Mathematics'.

In this paper the author proves the following remarkable theorem: A group G is a homomorph of some knot group if and only if G is finitely generated and has weight at most one. The weight of a group is the smallest n such that there exist n group elements whose normal closure is the whole group. Knot groups have weight one, and the homomorph of a weight one group has weight one. Knot groups are finitely generated and the homomorph of a finitely generated group is finitely generated, so the power of the theorem is evident; finite simple groups, for example, are homomorphs of knot groups.

A well-known theorem in the theory of 3-manifolds says that isomorphisms between (Haken) 3-manifold groups are in most cases induced by homeomorphisms. All the cases in which this is not true are well understood. In fact, it is well understood when a homotopy equivalence between Haken 3-manifolds fails to be a homeomorphism. The authors are interested in finding out when essential maps between knot spaces fail to be homeomorphisms. The answer is again that this happens much less than expected.

... Fico invited me to the Institute of Mathematics, he met me at the airport in his nondescript car, and we spent three months working together. This was one of the experiences that every time it is repeated, on the occasion of our mutual encounters, gives me greater pleasure. Anyone who has been lucky enough to talk to Fico about mathematics knows this. We talked about it in the car; on the street; at the dentist's surgery; buying tortillas; playing baseball; in his house, surrounded by children and with his better half, the ineffable Susana, who, I remember, made all kinds of extra-mathematical comments. Finally, everywhere. But Fico did not lose his temper or the thread. It was patience in person. And from one day to the next, he continued to keep his pulse on whatever the problem was.

... Fico, with his dedication, prestige and editorial skills, gave credibility to the Bulletin.

Fico has been a leading topologist, and in general, a leading mathematician for over 45 years. He has been a pillar in the development of a research community of mathematics in México, and more particularly, he has played an essential rôle in the development of topology in México. Fico has a deep knowledge of many and varied branches of mathematics, and his contributions to the topology of low-dimensional manifolds are influential and wide ranging.

The influence of a great teacher and superb mathematician is measured by his published work, by the published works of his disciples, and, perhaps most important, for the mathematical atmosphere it created and helped to maintain. I think that in these three facets Fico's work is equally memorable.

Various international tributes and congresses of the highest level have been organised in Fico's honour, with the presence in Mexico of world leaders in the area. This has put Mexico on the map of world mathematics in the area, and has opened multiple doors for young Mexicans. ... His in-depth knowledge of various areas of mathematics amazes everyone who has had the opportunity to speak with him. When you ask him anything, he doesn't answer immediately, but ponders it carefully, and when he does give his answer, a few minutes, hours, or days later, it is invariably much more interesting and profound than the original question. Exemplary academic, with an amazing ability to listen, understand and contribute ideas, regardless of the subject, without expecting anything in return. His careful intellectual ethics has been an example for many generations of mathematicians, and has earned him the respect, affection, and admiration of the national and international mathematical community.

Fico is a mathematician who has dedicated his life to high quality research. He published his first paper as an undergraduate student and did an exceptional doctoral thesis. He continued to do high-quality research after his doctorate, as can be seen from his articles published in the 'Annals of Mathematics', which is why, when the National System of Researchers was formed in 1984, Fico received the level III distinction in that system, which he has maintained ever since. His work is widely recognised abroad, and his articles have received more than 600 citations. Fico has been a reference for the new generations that have come to the Institute of Mathematics since the 1980s, since he has maintained his style, that of publishing only transcendent and high-quality articles.

To my beloved parents, Susana and Fico, who have loved, helped and supported me unconditionally all my life. Thanks so much for believing in me, for bringing me to life, for everything.