### Biography

Leopoldo Nachbin, Jewish Brazilian mathematician** **(Recife 07 January 1922 – Rio de Janeiro 03 April 1993)

Son of Polish father and Austrian mother

### ACHIEVEMENTS

Published 110 papers

Performed pioneer works about holomorphy in infinite dimension

Realized the first systematic study of topological vector spaces (1948)

Presented required and sufficient conditions in order to a continuous functions space to be bornological

Defined certain weighted spaces and compact element in a lattice

Initiated the study of topological ordered spaces

Demonstrated that a distributive lattice displaying elements 0 and 1 where all prime filter is maximal is a Boolean algebra (1947)

Extended Stone-Weierstrass theorem to differentiable functions

With J.B. Prolla & S. Machado proved that the polynomials of finite type from a real locally convex space into another are dense in the space of all continuous function with the compact open topology

Established conditions for a continuous functions subspace of compact basis be located under a subalgebra of continuous functions algebra

Nachbin theorem

An extension of the notion of integral functions of the finite exponential type. Anais Acad. Bras. Ciencias 16:143-7, 1944.

Obtained the concept of semi-uniform structures.

Sur les espaces topologiques ordonnés. C.R. Acad. Sci. Paris 226:381-2, 1948.

Introduced concept of compactness

On a characterization of the lattice of all ideals in a Bollean ring. Fund. Mathematicae 36:137-142, 1949.

Proved that every non-discrete valuable topological division ring is strictly minimal

On strictly minimal topological division rings. Bull. Amer. Math. Soc. 55:1128-36, 1949.

Nachbin-Goodner-Kelley theorem

A theorem of the Hahn-Banach type for linear transformations. Trans. Amer.Math. Soc. 68:28-46, 1950.

Hewitt-Nachbin spaces

On the continuity of positive linear transformations. Proc. Intern. Congress of Math. Cambridge, Mass. 1950. Vol I, Amer. Math. Soc, Providence, R.I., 464-5, 1952.

Nachbin-Shirota theorem

Topological Vector Spaces of Continuous Functions. Proceed. National Acad. Sciences 40:471-2, 1954.

Formulated a conjecture about Weierstrass approximation theorem

Formulação geral do teorema de aproximação de Weierstrass para funções diferenciáveis, Tópicos de topologia, Expos. De Mat 3, Univ. Ceará, Fortaleza, Ceará, 1961.

Bernstein-Nachbin approximation

Weighted approximation over topological spaces and the Bernstein problem over finite dimensional vector spaces. Topology 3, Suppl. 1:125-30, 1964.

Introduced topology Tau omega

On the topology of the space of all holomorphic functions on a given open subset, Indag. Math. 29:366-8, 1967.

Introduced Topology Tau epsilon

Sur les espaces vetorels topologiques d’applications continues. C.R. Acad. Sci. Paris 271:596-8, 1970.

Authored the thesis Topologia e Ordem (in English Topology and Order) in 1950, later translated to English and edited by Van Nostrand from Princeton in 1965. This book displayed new concepts such as a completely regularly ordered space and first to explicity define the notion of a pospace

Authored The Haar Integral (1965), worldwide used in mathematical courses

### INTRODUCED

Notion of fundamental weight

Concept of quase-uniform space

Ideal completion of a sup-semilattice

Notion of holomorphy type

Holomorphic Mackey spaces ((with J.A. Barroso & M.C. Matos)

Concept of uniform holomorphy

Concept of weighted spaces of continuous real-valued functions

Concept of locally weighted convex spaces of continuous scalar functions on a topological space

Concept of localizability in weighted approximation problem

### HONORS

Houssay Prize from OAS (1982)

George Eastman Professor of Mathematics, University of Rochester (1967) created for him

First Brazilian Mathematician invited to give conference at International Congress of Mathematicians in Stockholm (1962)

### EPONYMY

Nachbin uniform structure

Nachbin lemma

Nachbin family

Nachbin topology

Nachbin compactification

Nachbin property

Urysohn-Nachbin extension and separation theorems

Nachbin cones

Nachbin ported topologies

Nachbin m-algebras

Nachbin polynomial

### LINKS

WWW.mu.sbm.org.br/Conteudo/n16/n16_Artigo02.pdf (in Portuguese)