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Topic: Kazimierz Kuratowski

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	Kazimierz Kuratowski - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-07)
		June 18, 1980 in Warsaw, Poland) was a Polish mathematician.
		Kazimierz was since 1927 professor at the Politechnika Lwowska in Lwów and since 1934 at the Warsaw University.
		From 1948 until 1967 he was director of the Institute of Mathematics of the Polish Academy of Science and was also a long-term chairman of the Polish and the International Mathematics Society.
	en.wikipedia.org /wiki/Kazimierz_Kuratowski (154 words)

	Kazimierz Kuratowski, Mathematician
		Kuratowski became secretary to the mathematics committee and his report was made in 1937.
		Kuratowski now took on the role of leader in this rebuilding process and, through the Polish Mathematical Society of which he was president for eight years immediately following the war, he set about arguing for the implementation of the recommendations of his 1937 report.
		Kuratowski was appointed the Director of the Mathematical Institute of the Polish Academy of Sciences in 1949, a position he held for 19 years.
	www.polishwashington.com /prominent-poles/Kazimierz.Kuratowski.htm (1255 words)

	Kazimierz Kuratowski (Site not responding. Last check: 2007-10-07)
		When Kazimierz Kuratowski was born, all secondary schooling in Poland was in Russian.
		Kuratowski was appointed as a professor at the Technical University of Lvov in 1927.
		Kuratowski was appointed the Director of the Mathematical Institute of the Polish Academy of Sciences in 1949.
	www.stetson.edu /~efriedma/periodictable/html/Kr.html (951 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-07)
		Kazimierz Dolny is a little town in eastern Poland, with 2,700 inhabitants (1998), situated in the Pulawy County of the Lublin Voivodship, on the banks of Vistula river.
		Kazimierz Michałowski (1901 - 1981) was a Polish archeologist and Egyptologist, founder of Nubiology.
		Kazimierz Proszyński (1875 - 1945) was a Polish inventor.
	teamsweb.info /browse.php?title=K/KA/KAZ (3554 words)

	KURATOWSKI
		Kuratowski was born on 2nd Feb 1896 in Warsaw, Poland.
		In 1921, Kuratowski was awarded his doctorate, but sadly his supervisor Janiszewski had died in 1920.
		E Marczewski, "On the papers of Kazimierz Kuratowski in set theory and measure theory (Polish)", Wiadomosci matematyczne (2) 3 (1960), 239-244.
	www.algana.co.uk /FamousNames/K/kuratowski.htm (287 words)

	Kuratowski (Site not responding. Last check: 2007-10-07)
		Kazimierz Kuratowski's father, Marek Kuratowski was a leading lawyer in Warsaw.
		Kuratowski (and Steinhaus) sometimes joined their colleagues in the Scottish Café but he had left Lvov before the mathematicians began writing down the problems in the Scottish Book.
		Kuratowski was appointed the Director of the Mathematical Institute of the
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Kuratowski.html (2155 words)

	iqexpand.com (Site not responding. Last check: 2007-10-07)
		Look for Kazimierz kuratowski in the Commons, our repository for free images, music, sound, and video.
		Prominent Poles - Kazimierz Kuratowski, Mathematician Prominent Poles Kazimierz Kuratowski, Mathematician Born: February 2, 1896, in Warsaw, Poland Died: June 18, 1980, in Warsaw, Poland Accomplishments:...
		Topology Conference: in honor of Kazimierz Kuratowski and Karol Borsuk, Warsaw University and the Institute of Mathematics of Polish Academy of...
	kazimierz_kuratowski.iqexpand.com (313 words)

	Kuratowski closure axioms - Wikipedia, the free encyclopedia
		In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms which can be used to define a topological structure on a set.
		They were first introduced by Kazimierz Kuratowski, in a slightly different form that applied only to Hausdorff spaces.
		A similar set of axioms can be used to define a topological structure using only the dual notion of interior operator.
	en.wikipedia.org /wiki/Kuratowski_closure_axioms (220 words)

	Kuratowski's Closure Operation in Topology
		The Polish mathematician Kazimierz (Casimir) Kuratowski (1896-1980) developed a radically different approach to specifying a topology for a set.
		Kuratowski considered particular functions from the set of subsets of S to the set of subsets of S; i.e.,
		Theorem K1: A Kuratowski closure operation on the power set of a set S generates a collection of subsets of S which satisfy the closed set conditions and thus establish a topology for the set S. (To be continued.)
	www.applet-magic.com /kuratowski.htm (584 words)

	Honorary doctorate for William A. Kirk
		I studied the topology of Kazimierz Kuratowski and Wacław Sierpiński, the functional analysis of Stefan Banach, and the set theory of Alfred Tarski.
		In the fall of that year Kazimierz Goebel arrived in Iowa City to spend the year at the University of Iowa under the aegis of a Kościuszko Foundation fellowship.
		The conference was held in the beautiful village of Kazimierz Dolny in June, 1997.
	math.umcs.lublin.pl /KIRK1/lectKirk.htm (2117 words)

	PIGALE Library
		Conference dedicated to the memory of Kazimierz Kuratowski.
		This algorithm is the last part of the two step linear time Kuratowski finding algorithm implemented in PIGALE (``Public Implementation of a Graph Algorithm Library and Editor'', freely available at http://pigale.sourceforge.org).
		We give a characterization of DFS cotree-critical graphs which is central to the linear time Kuratowski finding algorithm implemented in PIGALE (Public Implementation of a Graph Algorithm Library and Editor) by the authors, and deduce an algorithm for finding a Kuratowski subdivision in a DFS cotree-critical graph.
	pigale.sourceforge.net /bibliography.html (804 words)

	Kazimierz Kuratowski -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		Kazimierz Kuratowski -- Facts, Info, and Encyclopedia article
		Kazimierz Kuratowski (born February 2 1896, (The capital and largest city of Poland; located in central Poland) Warsaw, died June 18, 1980, (The capital and largest city of Poland; located in central Poland) Warsaw)
		Among his contributions to (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics are:
	www.absoluteastronomy.com /encyclopedia/k/ka/kazimierz_kuratowski.htm (194 words)

	STANISŁAW ZAREMBA
		Kazimierz Paulin Żorawski (1866-1953) was a student of Sophus Lie and brought fundamental ideas of his master, of course first of all those related to theory of continuous groups (called now Lie groups), implementing them creatively in Kraków.
		Kazimierz Żorawski was the supervisor of the Ph.D. thesis of Franciszek Leja (1885-1979); among his pupils there were Władysław Ślebodziński (1884-1972) and Antoni Hoborski (1879-1940) who was simultaneously scientifically close to Zaremba, obtaining Ph.D. and habilitation under Zaremba’s supervision, and then turning to differential geometry, the field from Żorawski’s general area of interest.
		[12] A.Pelczar, Kazimierz Paulin Żorawski i Stanisław Zaremba (Kazimierz Paulin Żorawski and Stanisław Zaremba [in Polish]) [in:]
	wings.buffalo.edu /info-poland/web/sci_health/math/Zaremba/Zaremba.htm (4432 words)

	Colorful Mathematics: Part I (Site not responding. Last check: 2007-10-07)
		These graphs are known as the Kuratowski graphs because the Polish mathematician Kazimierz Kuratowski (1896-1980) showed that in a precise sense, every non-planar graph "contains" a copy of one of these two.
		For studying planarity and coloring problems associated with graphs, it has been very helpful to be able to start with one graph and transform it into another graph with related properties.
		The answer to this question, with regard to the plane, can be arrived at by purely combinatorial aspects of the graph's description.
	80-www.ams.org.library.uor.edu /featurecolumn/archive/coloring2.html (1188 words)

	Book review: Handbook of the History of General Topology, Volume 2
		The individual contributions and influences of Waclaw Sierspinski (1882-1969) and of Kazimierz Kuratowski (1896-1980), are discussed by Ryszard Engelking, and R.
		The Warsaw School of Mathematics was an idea of Sierpinski, Janiszewski and Mazurkiewicz, when they met in the Warsaw University and decided to concentrate mathematical research on set theory and its various applications, which were new domains and it would be easier to catch up with world mathematics.
		Later on, the younger Kuratowski joined the group and in 1932, by his initiative, the series Monografie Matematyczne was launched.
	at.yorku.ca /t/o/p/d/41.htm (1580 words)

	Talk:Planar graph - TheBestLinks.com - Graph theory, Kazimierz Kuratowski, If and only if, Vertex, ... (Site not responding. Last check: 2007-10-07)
		Talk:Planar graph - TheBestLinks.com - Graph theory, Kazimierz Kuratowski, If and only if, Vertex,...
		Talk:Planar graph, Graph theory, Planar graph, Kazimierz Kuratowski...
		In Kazimierz Kuratowski, the following version of Kuratowski's theorem was given:
	www.thebestlinks.com /Talk__3A__Planar_graph.html (662 words)

	Ajdukiewicz, Kazimierz -- Encyclopædia Britannica
		He is credited with developing in 1920 the first deductive theory for the study of logic based on syntax.
		"Ajdukiewicz, Kazimierz." Encyclopædia Britannica from Encyclopædia Britannica Premium Service.
		More results on "Ajdukiewicz, Kazimierz" when you join.
	www.britannica.com /eb/article-9005246?tocId=9005246 (468 words)

	The world's top planar graph websites
		A finite graph is planar if and only if it does not contain a subgraph that is an expansion of
		A far-reaching generalization of Kuratowski's theorem is given by the Robertson-Seymour theorem; in the language of this theorem,
		This is the smallest non-outerplanar graph: a theorem similar to Kuratowski's states that a finite graph is outerplanar if and only if it does not contain a subgraph that is an expansion of
	dirs.org /wiki-article-tab.cfm/planar_graph (1076 words)

	Do Unto Others Project-Church of the Science of God (Site not responding. Last check: 2007-10-07)
		It is conceivable that such experimentation might disprove some outstanding conjectures by yielding a graph with a crossing number that is less than the expected value.
		Graphs with a crossing number of zero are fully explained by Kuratowski’s theo-rem which was proved by Polish mathematician Kazimierz Kuratowski.
		Such graphs are planar—the edges connecting the nodes do not cross one another at all.
	www.dountoothers.org /torusgrid.html (1326 words)

	Tetmajer, Kazimierz -- Encyclopædia Britannica
		in full Kazimierz Przerwa Tetmajer poet and short-story writer who was a member of the Young Poland movement.
		"Tetmajer, Kazimierz." Encyclopædia Britannica from Encyclopædia Britannica Premium Service.
		More results on "Tetmajer, Kazimierz" when you join.
	www.britannica.com /eb/article-9071840 (500 words)

	Polish Great mathematicians (Site not responding. Last check: 2007-10-07)
		Members of this school were: Wacław Sierpinski, Kazimierz Kuratowski, Edward Marczewski, Bronisław Knaster, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stanisław Saks, Karol Borsuk, Roman Sikorski
		Members of the Warsaw topology group who emigrated in the 1930's: Nachman Aronszajn (1907-1980) and Samuel Eilenberg (now in New York).
		In the 20th century, Cracow became a center of classical analysis, differential equations and analytic functions.
	www.impan.gov.pl /Great/shools.html (352 words)

	Math 6021 (Site not responding. Last check: 2007-10-07)
		Take a look at a brief biography of Stefan Mazurkiewicz, one of those for whom the celebrated Knaster-Kuratowski-Mazurkiewicz Theorem is named.
		You can also read about the life of Kazimierz Kuratowski.
		Have a look at your grade for the course.
	www.math.gatech.edu /~cain/summer00/m6021.html (468 words)

	The Mathematics Genealogy Project - Kazimierz Kuratowski
		Click here to see the students listed in chronological order.
		According to our current on-line database, Kazimierz Kuratowski has 2 students and 37 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	genealogy.math.ndsu.nodak.edu /html/id.phtml?id=24546&fChrono=1 (99 words)

	Institute of General Semantics: Pula, GS Bibliography (Site not responding. Last check: 2007-10-07)
		Kuratowski, Kazimierz, Fifty Years of Polish Mathematics: Remembrances and Reflections.
		Kuratowski, himself one of the group he tells about, gives an eyewitness account of the very human side of the mathematical school which influenced Korzybski’s formulations.
		Laszlo, Ervin, Introduction to Systems Theory: Toward a New Paradigm of Contemporary Thought.
	learn-gs.org /library/rpp-bib.htm (7810 words)

	The U of MT -- Mansfield Library LangFing Czech & Polish
		-- Tokyo : International House of Japan Library, 1972 RID: 72-188196 ITEM #: dut00110 491.8532 The Kosciuszko Foundation dictionary : English-Polish, Polish-English / by K86 Kazimierz Bulas and Francis J. Whitfield.
		-- Warszawa : X K94 RID: 34-9444 ITEM #: pol00015 511.3 Kuratowski, Kazimierz, 1896- K96t Teoria mnogosci.
		-- Warszawa : RID: --- ITEM #: pol00024 517 Kuratowski, Kazimierz, 1896- K96w Wyklady rachunku rozniczkowego i calkowego.
	www.lib.umt.edu /guide/lang/czechdeh.htm (2032 words)

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