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List Of Things Named After Wacław Sierpiński
This is a (partial) list of things named after Wacław Sierpiński (1882–1969), a Polish mathematician known especially for his contributions to set theory, number theory, theory of functions, and topology: Mathematics * Sierpinski triangle * Sierpinski carpet * Sierpinski curve * Sierpinski number * Sierpiński cube *Sierpiński's constant *Sierpiński set * Sierpiński game *Sierpiński space * Sierpiński's theorem on metric spaces * Sierpiński problem * Prime Sierpiński problem * Extended Sierpiński problem * Sierpiński-Riesel problem Other * Sierpinski (crater), a crater on the Moon * Sierpiński Medal, an award conferred by the University of Warsaw and the Polish Mathematical Society The Polish Mathematical Society () is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). History The society was ... See also * References {{reflist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wacław Sierpiński
Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a Polish mathematician. He was known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions, and topology. He published over 700 papers and 50 books. Three well-known fractals are named after him (the Sierpiński triangle, the Sierpiński carpet, and the Sierpiński curve), as are Sierpiński numbers and the associated Sierpiński problem. Early life and education Sierpiński was born in 1882 in Warsaw, Congress Poland, to a doctor father Konstanty and mother Ludwika (''née'' Łapińska). His abilities in mathematics were evident from childhood. He enrolled in the Department of Mathematics and Physics at the University of Warsaw in 1899 and graduated five years later. In 1903, while still at the University of Warsaw, the Department of Mathematics and Physics offered a prize for the best essay from a student on Vorono ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sierpiński Set
In mathematics, a Sierpiński set is an uncountable subset of a real vector space whose intersection with every measure-zero set is countable. The existence of Sierpiński sets is independent of the axioms of ZFC. showed that they exist if the continuum hypothesis is true. On the other hand, they do not exist if Martin's axiom for ℵ1 is true. Sierpiński sets are weakly Luzin sets but are not Luzin sets . Example of a Sierpiński set Choose a collection of 2ℵ0 measure-0 subsets of R such that every measure-0 subset is contained in one of them. By the continuum hypothesis, it is possible to enumerate them as ''S''''α'' for countable ordinals ''α''. For each countable ordinal ''β'' choose a real number ''x''''β'' that is not in any of the sets ''S''''α'' for ''α'' < ''β'', which is possible as the union of these sets has measure 0 so is not the whole of R. Then the uncountable set ''X'' of all these real numbers ''x''''β'' has only a countable nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Warsaw
The University of Warsaw (, ) is a public university, public research university in Warsaw, Poland. Established on November 19, 1816, it is the largest institution of higher learning in the country, offering 37 different fields of study as well as 100 specializations in humanities, Engineering, technical, and natural sciences. The University of Warsaw consists of 126 buildings and educational complexes with over 18 faculties: biology, chemistry, medicine, journalism, political science, philosophy, sociology, physics, geography, regional studies, geology, history, applied linguistics, philology, Polish language, pedagogy, economics, law, public administration, psychology, applied social sciences, management, mathematics, computer science, and mechanics. Among the university's notable alumni are heads of state, prime ministers, Nobel Prize laureates, including Joseph Rotblat, Sir Joseph Rotblat and Olga Tokarczuk, as well as several historically important individuals in their res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moon
The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar day) that is synchronized to its orbital period (Lunar month#Synodic month, lunar month) of 29.5 Earth days. This is the product of Earth's gravitation having tidal forces, tidally pulled on the Moon until one part of it stopped rotating away from the near side of the Moon, near side, making always the same lunar surface face Earth. Conversley, the gravitational pull of the Moon, on Earth, is the main driver of Earth's tides. In geophysical definition of planet, geophysical terms, the Moon is a planetary-mass object or satellite planet. Its mass is 1.2% that of the Earth, and its diameter is , roughly one-quarter of Earth's (about as wide as the contiguous United States). Within the Solar System, it is the List of Solar System objects by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sierpinski (crater)
Sierpinski is a lunar impact crater on the far side of the Moon. It lies to the southeast of the huge walled plain Gagarin, and to the northwest of the crater O'Day and the Mare Ingenii. This crater has undergone some wear, particularly along the southwest where Sierpinski Q intrudes slightly into the inner wall. The rim is higher and the inner wall wider along the eastern side. There is a prominent ridge within the interior that extends from near the midpoint to the northern inner wall. There are several small craters along the inner wall in the north and northwest. Only a small portion of the interior floor along the western half is relatively level. Satellite craters By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Sierpinski. References * * * * * * * * * * * * {{refend External links Lunar Map 103 showing Sierpinski and surroundings (Regional maps at the Lunar and Planetary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sierpiński Number
In number theory, a Sierpiński number is an odd natural number ''k'' such that k \times 2^n + 1 is composite for all natural numbers ''n''. In 1960, Wacław Sierpiński proved that there are infinitely many odd integers ''k'' which have this property. In other words, when ''k'' is a Sierpiński number, all members of the following set are composite: :\left\. If the form is instead k \times 2^n - 1 , then ''k'' is a Riesel number. Known Sierpiński numbers The sequence of currently ''known'' Sierpiński numbers begins with: : 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, 965431, 1259779, 1290677, 1518781, 1624097, 1639459, 1777613, 2131043, 2131099, 2191531, 2510177, 2541601, 2576089, 2931767, 2931991, ... . The number 78557 was proved to be a Sierpiński number by John Selfridge in 1962, who showed that all numbers of the form have a factor in the covering set . For another known Sierpiński number, 271129, the covering set is . Most curre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sierpiński's Theorem On Metric Spaces
In mathematics, Sierpiński's theorem is an isomorphism theorem concerning certain metric spaces, named after Wacław Sierpiński who proved it in 1920. It states that any countable metric space without isolated points is homeomorphic to \mathbb (with its standard topology). Examples As a consequence of the theorem, the metric space \mathbb^2 (with its usual Euclidean distance) is homeomorphic to \mathbb, which may seem counterintuitive. This is in contrast to, e.g., \mathbb^2, which is not homeomorphic to \mathbb. As another example, \mathbb \cap , 1/math> is also homeomorphic to \mathbb, again in contrast to the closed real interval , 1/math>, which is not homeomorphic to \mathbb (whereas the open interval (0, 1) is). References {{ reflist , refs = {{ cite journal , last = Sierpiński , first = Wacław , title = Sur une propriété topologique des ensembles dénombrables denses en soi , date = 1920 , journal = Fundamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sierpiński Space
In mathematics, the Sierpiński space is a finite topological space with two points, only one of which is closed. It is the smallest example of a topological space which is neither trivial nor discrete. It is named after Wacław Sierpiński. The Sierpiński space has important relations to the theory of computation and semantics, because it is the classifying space for open sets in the Scott topology. Definition and fundamental properties Explicitly, the Sierpiński space is a topological space ''S'' whose underlying point set is \ and whose open sets are \. The closed sets are \. So the singleton set \ is closed and the set \ is open (\varnothing = \ is the empty set). The closure operator on ''S'' is determined by \overline = \, \qquad \overline = \. A finite topological space is also uniquely determined by its specialization preorder. For the Sierpiński space this preorder is actually a partial order and given by 0 \leq 0, \qquad 0 \leq 1, \qquad 1 \leq 1. Topol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Game
In mathematics, a topological game is an infinite game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is generally discrete, but the plays may have Transfinite number, transfinite lengths, and extensions to continuum time have been put forth. The conditions for a player to win can involve notions like topological closure and wikt:convergence, convergence. It turns out that some fundamental topological constructions have a natural counterpart in topological games; examples of these are the Baire property, Baire spaces, completeness and convergence properties, separation properties, covering and base properties, continuous images, Suslin sets, and singular spaces. At the same time, some topological properties that arise naturally in topological games can be generalized beyond a game-theoretic context: by virtue of this duality, topological games ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sierpiński's Constant
Sierpiński's constant is a mathematical constant usually denoted as ''K''. One way of defining it is as the following limit: :K=\lim_\left sum_^ - \pi\ln n\right/math> where ''r''2(''k'') is a number of representations of ''k'' as a sum of the form ''a''2 + ''b''2 for integer ''a'' and ''b''. It can be given in closed form as: :\begin K &= \pi \left(2 \ln 2+3 \ln \pi + 2 \gamma - 4 \ln \Gamma \left(\tfrac\right)\right)\\ &=\pi \ln\left(\frac\right)\\ &=\pi \ln\left(\frac\right)\\ &= 2.58498 17595 79253 21706 58935 87383\dots \end where \varpi is the lemniscate constant and \gamma is the Euler-Mascheroni constant. Another way to define/understand Sierpiński's constant is, Let r(n) denote the number of representations of n by k squares, then the Summatory Function of r_2(k)/k has the Asymptotic expansion \sum_^=K+\pi\ln n+o\!\left(\frac\right), where K=2.5849817596 is the Sierpinski constant. The above plot shows \left(\sum_^\right)-\pi\ln n, with the value ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
