|
Zoltán Tibor Balogh
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 products, 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.Z. Balogh, Non-shrinking open covers and K. Morita's duality conjectures, '' Topology Appl.'', 115 (2001) 333-341 References External linksMemorial with photograph [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hungary
Hungary ( hu, Magyarország ) is a landlocked country in Central Europe. Spanning of the Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia and Slovenia to the southwest, and Austria to the west. Hungary has a population of nearly 9 million, mostly ethnic Hungarians and a significant Romani minority. Hungarian, the official language, is the world's most widely spoken Uralic language and among the few non-Indo-European languages widely spoken in Europe. Budapest is the country's capital and largest city; other major urban areas include Debrecen, Szeged, Miskolc, Pécs, and Győr. The territory of present-day Hungary has for centuries been a crossroads for various peoples, including Celts, Romans, Germanic tribes, Huns, West Slavs and the Avars. The foundation of the Hungarian state was established in the late 9th century AD with the conquest of the Carpathian Basin by Hungar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1953 Births
Events January * January 6 – The Asian Socialist Conference opens in Rangoon, Burma. * January 12 – Estonian émigrés found a government-in-exile in Oslo. * January 14 ** Marshal Josip Broz Tito is chosen President of Yugoslavia. ** The CIA-sponsored Robertson Panel first meets to discuss the UFO phenomenon. * January 15 – Georg Dertinger, foreign minister of East Germany, is arrested for spying. * January 19 – 71.1% of all television sets in the United States are tuned into ''I Love Lucy'', to watch Lucy give birth to Little Ricky, which is more people than those who tune into Dwight Eisenhower's inauguration the next day. This record has yet to be broken. * January 20 – Dwight D. Eisenhower is sworn in as the 34th President of the United States. * January 24 ** Mau Mau Uprising: Rebels in Kenya kill the Ruck family (father, mother, and six-year-old son). ** Leader of East Germany Walter Ulbricht announces that agriculture will be col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zentralblatt MATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic. History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix Klein, the great ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morita Conjectures
The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. The conjectures, formulated by Kiiti Morita in 1976, asked # If X \times Y is normal for every normal space ''Y'', is ''X'' a discrete space? # If X \times Y is normal for every normal P-space#P-spaces in the sense of Morita, P-space ''Y'', is ''X'' metrizable? # If X \times Y is normal for every normal countably paracompact space ''Y'', is ''X'' metrizable and sigma-locally compact? The answers were believed to be affirmative. Here a normal P-space ''Y'' is characterised by the property that the product with every metrizable ''X'' is normal; thus the conjecture was that the converse holds. Keiko Chiba, Teodor C. Przymusiński, and Mary Ellen Rudin proved conjecture (1) and showed that conjectures (2) and (3) cannot be proven false under the standard Zermelo–Fraenkel set theory, ZFC axioms for mathematics (specifically, that the conjectures hold under the axiom o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paracompact
In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by . Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits partitions of unity subordinate to any open cover. Sometimes paracompact spaces are defined so as to always be Hausdorff. Every closed subspace of a paracompact space is paracompact. While compact subsets of Hausdorff spaces are always closed, this is not true for paracompact subsets. A space such that every subspace of it is a paracompact space is called hereditarily paracompact. This is equivalent to requiring that every open subspace be paracompact. Tychonoff's theorem (which states that the product of any collection of compact topological spaces is compact) does not generalize to paracompact spaces in that the product of paracompact spaces need not be paracompact. Howeve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. These conditions are examples of separation axioms and their further strengthenings define completely normal Hausdorff spaces, or T5 spaces, and perfectly normal Hausdorff spaces, or T6 spaces. Definitions A topological space ''X'' is a normal space if, given any disjoint closed sets ''E'' and ''F'', there are neighbourhoods ''U'' of ''E'' and ''V'' of ''F'' that are also disjoint. More intuitively, this condition says that ''E'' and ''F'' can be separated by neighbourhoods. A T4 space is a T1 space ''X'' that is normal; this is equivalent to ''X'' being normal and Hausdorff. A completely normal space, or , is a topological space ''X'' such that every subspace of ''X'' with subspace topology is a normal space. It turns out that ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dowker Space
In the mathematical field of general topology, a Dowker space is a topological space that is T4 but not countably paracompact. They are named after Clifford Hugh Dowker. The non-trivial task of providing an example of a Dowker space (and therefore also proving their existence as mathematical objects) helped mathematicians better understand the nature and variety of topological spaces. Equivalences Dowker showed, in 1951, the following: If ''X'' is a normal T1 space (that is, a T4 space), then the following are equivalent: * ''X'' is a Dowker space * The product of ''X'' with the unit interval is not normal. * ''X'' is not countably metacompact. Dowker conjectured that there were no Dowker spaces, and the conjecture was not resolved until Mary Ellen Rudin constructed one in 1971. Rudin's counterexample is a very large space (of cardinality \aleph_\omega^). Zoltán Balogh gave the first ZFC construction of a small (cardinality continuum) example, which was more well-behaved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 \mathfrak c (lowercase fraktur "c") or , \mathbb R, . The real numbers \mathbb R are more numerous than the natural numbers \mathbb N. Moreover, \mathbb R has the same number of elements as the power set of \mathbb N. Symbolically, if the cardinality of \mathbb N is denoted as \aleph_0, the cardinality of the continuum is This was proven by Georg Cantor in his uncountability proof of 1874, part of his groundbreaking study of different infinities. The inequality was later stated more simply in his diagonal argument in 1891. Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if, and only if, there exists a bijective function between them. Between any two real numbers ''a'' \mathfrak c . Alternative explanation for 𝔠 = 2ℵ0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
