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Topic: Felix Hausdorff


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In the News (Wed 24 Apr 19)

  
  Felix Hausdorff - Wikipedia, the free encyclopedia
Felix Hausdorff (November 8, 1868 – January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory and functional analysis.
He defined and studied partially ordered sets, Hausdorff spaces, and the Hausdorff dimension, proved the Hausdorff maximality theorem, solved what is now called the Hausdorff moment problem, and published philosophical and literary works under the pseudonym "Paul Mongré".
Hausdorff studied in Leipzig and taught mathematics there until 1910, when he became professor of mathematics in Bonn.
en.wikipedia.org /wiki/Felix_Hausdorff   (205 words)

  
 Hausdorff, Felix - Hutchinson encyclopedia article about Hausdorff, Felix   (Site not responding. Last check: 2007-11-07)
Hausdorff was born in Breslau, Germany (now Wrocław, Poland), and studied at Berlin, Freiburg, and Leipzig.
Hausdorff formulated a theory of topological and metric spaces, proposing that such spaces be regarded as sets of points and sets of relations among the points, and introduced the principle of duality.
This principle states that an equation between sets remains valid if the sets are replaced by their complements and the symbol for union is exchanged for that of intersection.
encyclopedia.farlex.com /Hausdorff,+Felix   (268 words)

  
 Hausdorff biography   (Site not responding. Last check: 2007-11-07)
Felix was born into a wealthy family and this had quite an influence on his life and career since he never had the problem of having to work to support himself financially.
Hausdorff studied at Leipzig University under Heinrich Bruns and Adolph Mayer, graduating in 1891 with a doctorate in applications of mathematics to astronomy.
Hausdorff married Charlotte Sara Goldschmidt in Leipzig in 1899.
www-groups.dcs.st-and.ac.uk /history/Biographies/Hausdorff.html   (1823 words)

  
 Felix Hausdorff
Felix Hausdorff (November 8, 1868 - January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory and functional analysis.
When the Nazis came to power, Hausdorff, a Jew, felt that as a respected university professor he was immune.
When in 1942 he could no longer avoid being sent to a concentration camp, he committed suicide together with his wife and sister-in-law.
www.ebroadcast.com.au /lookup/encyclopedia/fe/Felix_Hausdorff.html   (150 words)

  
 Hausdorff, Felix (1868-1942)
Among several concepts named after him is the Hausdorff dimension, which gives a way of assigning a fractional dimension to a curve or shape.
Hausdorff also published philosophical and literary works under the pseudonym "Paul Mongré." He studied at Leipzig and taught mathematics there until 1910, when he became professor of mathematics at Bonn.
When the Nazis came to power, Hausdorff, a Jew, felt that as a respected university professor he would be safe from persecution.
www.daviddarling.info /encyclopedia/H/Hausdorff_Felix.html   (236 words)

  
 Hausdorff - Wikipedia, the free encyclopedia
A Hausdorff space, when used as an adjective, as in "the real line is Hausdorff."
Felix Hausdorff, the German mathematician that Hausdorff spaces are named after.
Hausdorff dimension, a measure theoretic concept of dimension.
en.wikipedia.org /wiki/Hausdorff   (107 words)

  
 ipedia.com: Hausdorff dimension Article   (Site not responding. Last check: 2007-11-07)
The Hausdorff dimension (also: Hausdorff-Besicovitch dimension, capacity dimension and fractal dimension), introduced by Felix Hausdorff, gives a way to accurately measure the dimension of complicated sets such as fractals.
The Hausdorff dimension agrees with the ordinary (topological) dimension on "well-behaved sets", but it is applicable to many more sets and is not always a natural number.
The Hausdorff dimension should not be confused with the (similar) box-counting dimension.
www.ipedia.com /hausdorff_dimension.html   (750 words)

  
 Hausdorff dimension
The Hausdorff dimension, named after Felix Hausdorff, coincides with the more familiar notion of dimension in the case of well-behaved sets.
For example a straight line or an ordinary curve, such as a circle, has a Hausdorff dimension of 1; any countable set has a Hausdorff dimension of 0; and an n-dimensional Euclidean space has a Hausdorff dimension of n.
But a Hausdorff dimension is not always a natural number.
www.daviddarling.info /encyclopedia/H/Hausdorff_dimension.html   (217 words)

  
 Felix Hausdorff   (Site not responding. Last check: 2007-11-07)
Felix Hausdorff graduated from Leipzig in 1891, and then taught there until 1910 when he went to Bonn.
Hausdorff's main work was in topology and set theory.
Hausdorff worked at Bonn until 1935 when he was forced to retire by the Nazi regime.
www.stetson.edu /~efriedma/periodictable/html/Hf.html   (256 words)

  
 Hausdorff dimension - ExampleProblems
In mathematics, the Hausdorff dimension is an extended non-negative real number (that is a number in the closed infinite interval [0, ∞]) associated to any metric space.
It was introduced in 1918 by the mathematician Felix Hausdorff.
It is possible to try to do this directly for many sets (leading to so-called box counting dimension), but Hausdorff's insight was to approach the problem indirectly using the theory of measure developed earlier in the century by Henri Lebesgue and Constantin Caratheodory.
exampleproblems.com /wiki/index.php/Hausdorff_dimension   (1806 words)

  
 Hausdorff dimension
The Hausdorff dimension is a well-defined real number for any metric space M and we always have 0 ≤ d(M) ≤ ∞.
For example, the Cantor set (a zerodimensional topological space) is a union of two copies of itself, each copy shrunk by a factor 1/3; this fact can be used to prove that its Hausdorff dimension is ln(2)/ln(3) (see natural logarithm).
The Sierpinski triangle is a union of three copies of itself, each copy shrunk by a factor of 1/2; this yields a Hausdorff dimension of ln(3)/ln(2).
teachersparadise.com /ency/en/wikipedia/h/ha/hausdorff_dimension.html   (316 words)

  
 Hausdorff paradox -   (Site not responding. Last check: 2007-11-07)
In mathematics, the Hausdorff paradox, named after Felix Hausdorff, states that if you remove a certain countable subset of the sphere S², the remainder can be divided into three subsets A, B and C such that A, B, C and B ∪C are all congruent.
Sometimes the Hausdorff paradox refers to another theorem of Hausdorff which was proved in the same paper.
Hausdorff described these constructions in order to show that there can be no non-trivial, translation-invariant measure on the real line which assigns a size to all bounded subsets of real numbers.
psychcentral.com /psypsych/Hausdorff_paradox   (371 words)

  
 Hausdorff Distance
Felix Hausdorff (1868 -1942) devised a metric function between subsets of a metric space.
two sets are within Hausdorff distance r from each other iff any point of one set is within distance r from some point of the other set.
The Hausdorff metric h(A,B) is defined in terms of the neighborhoods.
www.cut-the-knot.org /do_you_know/Hausdorff.shtml   (687 words)

  
 Hausdorff distance
The two distances h(A, B) and h(B, A) are sometimes termed as forward and backward Hausdorff distances of A to B. Although the terminology is not stable yet among authors, eq.
Hausdorff distance gives an interesting measure of their mutual proximity, by indicating the maximal distance between any point of one polygon to the other polygon.
One of the main application of the Hausdorff distance is image matching, used for instance in image analysis, visual navigation of robots, computer-assisted surgery, etc. Basically, the Hausdorff metric will serve to check if a template image is present in a test image ; the lower the distance value, the best the match.
cgm.cs.mcgill.ca /~godfried/teaching/cg-projects/98/normand/main.html   (1810 words)

  
 OUP: Hausdorff on Ordered Sets: Plotkin
Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory.
Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets.
Also available from the AMS by Felix Hausdorff are the classic work, Grundzuge der Mengenlehre, and its English translation, Set Theory, as Volume 69 and Volume 119 in the AMS Chelsea Publishing series.
www.oup.co.uk /isbn/0-8218-3788-5   (610 words)

  
 Felix Hausdorff
Within a year of his appointment to Leipzig he was offered a post at Göttingen but, rather surprisingly given Göttingen's reputation, he turned it down.
In 1919 he introduced the notion of Hausdorff dimension, which was a real number lying between the topological dimension of an object and 3.
It is used to study objects such as Koch's curve.
umm.kou.edu.tr /math/felix_hausdorff.htm   (304 words)

  
 The Strange World of the Hausdorff Metric Geometry
In addition to his work with this metric, Hausdorff was also active in partially ordered sets, metric spaces, and Hausdorff dimension.
In 1942, after being forced to retire because of his Jewish heritage, Felix Hausdorff chose to take his own life rather than be placed in a concentration camp.
In this informal paper, we will introduce the Hausdorff metric, discuss some of its applications, and review the results obtained by the GVSU REU research groups on the geometry this metric imposes on the relevant space.
faculty.gvsu.edu /schlicks/HausdorffGeometry/H1.htm   (255 words)

  
 Atlas: Felix Hausdorff, his life and works. by S.D. Chatterji   (Site not responding. Last check: 2007-11-07)
Felix Hausdorff (1868-1942) has left a permanent mark in the history of 20th century mathematics.His collected works and some correspondence and hitherto unpulished material are being published in nine volumes by Springer Verlag; of these,volumes 2,4,7 have already appeared and volume 5 should appear soon.
In our talk,we shall give a broad survey of Hausdorff's life and work, highlighting the unusual challenge met by the edition of Hausdorff's Collected Papers.
The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqo-25.
atlas-conferences.com /cgi-bin/abstract/caqo-25   (108 words)

  
 Michiel Hazewinkel : Book review
The time of publishing (1992) this proceedings is both the anniversary of one of the main founders of topology - Felix Hausdorff and the hundredth anniversary of the publication of Poincare's first note on topology.
The beginning of general topology, also called "point set topology", dates fourteen years later when Frechet published the first abstract treatment of the subject in 1906.
This pioneering monograph secured his international reputation and it was a breakpoint from that the rapid development of classical topology begun.
homepages.cwi.nl /~mich/reviews/AAA_1083.html   (210 words)

  
 Colloquium of the Mathematical Sciences Group, Department of Computer Science, Saskatoon, 2002/03
This talk is dedicated to Felix Hausdorff, in memory of the 60th anniversary of his tragic death.
The space of minimal prime ideals of a commutative semiprime ring A with the hull-kernel topology (alias the Zariski topology) has long been known to be a zero-dimensional Hausdorff space and there are characterizations of when it is compact.
In case A = C(X) is the ring of all continuous real-valued on a Tychonoff space (i.e., a subspace of of a compact (Hausdorff) space), while there are many simply stated characterizations of spaces X with this property, they are not easy to use to answer natural questions about them.
math.usask.ca /fvk/collg7pe.htm   (4445 words)

  
 Middle East Open Encyclopedia: Felix Hausdorff   (Site not responding. Last check: 2007-11-07)
This is an extract from The Middle East Open Encyclopedia, made possible through the Wikimedia Foundation.
Iraq Museum International always displays the most recent published revision of the source article, Felix Hausdorff; all previous versions may be viewed here.
They link directly to authoring tools for you to start writing a particular article.
www.baghdadmuseum.org /ref/index.php?title=Felix_Hausdorff   (327 words)

  
 Hausdorff, Gèahler, Herrlich and Preuss (1992) Recent developments of general topology and its applications: ...
Hausdorff, Gèahler, Herrlich and Preuss (1992) Recent developments of general topology and its applications: International Conference in Memory of Felix Hausdorff (1868-1942), Berlin, March 22-28, 1992
Recent developments of general topology and its applications: International Conference in Memory of Felix Hausdorff (1868-1942), Berlin, March 22-28, 1992
There are no citations on file at this time.
www.getcited.org /?PUB=103139363&showStat=Citations   (55 words)

  
 Hausdorff spaces (from topology) --  Encyclopædia Britannica   (Site not responding. Last check: 2007-11-07)
A topological space is called Hausdorff (after the German mathematician Felix Hausdorff) if it satisfies the following condition: for each two points p, q there are disjoint open sets U(p), U(q) containing p and q, respectively.
Not all topological spaces are Hausdorff, but most of those that are seriously studied, including all those mentioned…
More from Britannica on "Hausdorff spaces (from topology)"...
www.britannica.com /eb/article-69116   (774 words)

  
 Find in a Library: Paradoxes of measures and dimensions originating in Felix Hausdorff's ideas
Find in a Library: Paradoxes of measures and dimensions originating in Felix Hausdorff's ideas
Paradoxes of measures and dimensions originating in Felix Hausdorff's ideas
WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
worldcatlibraries.org /wcpa/ow/2d0350c3a165a237a19afeb4da09e526.html   (69 words)

  
 The Mathematics Genealogy Project - Felix Hausdorff
Click here to see the students listed in chronological order.
According to our current on-line database, Felix Hausdorff has 3 students and 3 descendants.
If you have additional information or corrections regarding this mathematician, please use the update form.
www.genealogy.math.ndsu.nodak.edu /html/id.phtml?id=46991   (74 words)

  
 Find in a Library: Theory of sets and topology; in honour of Felix Housdorff (1868-1942
Theory of sets and topology; in honour of Felix Housdorff (1868-1942
by Felix Hausdorff; Günter Asser; J Flachsmeyer; Willi Rinow
To find this item in a library, enter a postal code, state, province, or country in the field above.
www.worldcatlibraries.org /wcpa/ow/f97956990a46bec5.html   (81 words)

  
 Recent Developments of General Topology and Its Applications: International Conference in Memory of Felix ...
Recent Developments of General Topology and Its Applications: International Conference in Memory of Felix Hausdorff
This item is temporarily unavailable from the publisher, but is expected in soon.
Place your order now and we will ship it as soon as it arrives.
www.ecampus.com /bk_detail.asp?isbn=3055014235   (62 words)

  
 SciTech Book News: Hausdorff on ordered sets.(Brief Article)(Book Review)@ HighBeam Research   (Site not responding. Last check: 2007-11-07)
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Between 1901 and 1909, Polish mathematician Felix Hausdorff (1868-1942) published seven papers in which he created a representation theory for ordered sets and investigated sets of real sequences partially ordered by eventual dominance,...
This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan.
www.highbeam.com /library/doc0.asp?DOCID=1G1:138410895&refid=holomed_1   (134 words)

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