Zoltán Tibor Balogh
Encyclopedia
Zoltán "Zoli" Tibor Balogh (December 7, 1953 – June 19, 2002) was a Hungarian
-born mathematician
, specializing in set-theoretic topology
. His father, Tibor Balogh, was also a mathematician. His best known work concerned solutions to problems involving normality
of product
s, most notably the first ZFC construction of a small (cardinality continuum
) Dowker space
. He also solved
Nagami's problem (normal
+ screenable does not imply paracompact), and the second and third Morita conjectures
about normality in products.
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
-born mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, specializing in set-theoretic topology
Set-theoretic topology
In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of ZFC. A famous problem is the normal Moore space question, a question in general topology that was the subject of intense research. The...
. His father, Tibor Balogh, was also a mathematician. His best known work concerned solutions to problems involving normality
Normal space
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space...
of product
Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology...
s, most notably the first ZFC construction of a small (cardinality continuum
Cardinality of the continuum
In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum. It is an infinite cardinal number and is denoted by |\mathbb R| or \mathfrak c ....
) Dowker space
Dowker space
A Dowker space is a topological space that is T4 but not countably paracompact.-Equivalences:If X is a normal T1 space , then the following are equivalent:* X is a Dowker space...
. He also solved
Nagami's problem (normal
Normal space
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space...
+ screenable does not imply paracompact), and the second and third Morita conjectures
Morita conjectures
The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. They asked# If X × Y is normal for every normal space Y, is X discrete?...
about normality in products.