Extends the Jordan curve theorem to characterize the inner and outer regions
In mathematics, the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves in the plane it is often referred to as the Jordan–Schoenflies theorem.
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mathematics, the Schoenfliesproblem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan...
crystallography, and for work in topology. Schoenflies was born in Landsberg an der Warthe (modern Gorzów, Poland). Arthur Schoenflies married Emma Levin (1868–1939)...
admits an exotic smooth structure is another open problem, closely linked to the Schoenfliesproblem in dimension four. Let M {\displaystyle M} be a Mazur...
Akbulut-Kirby 4-sphere, with relevance to the Andres-Curtis and Schoenfliesproblems", Topology, 30: 123–136, doi:10.1016/0040-9383(91)90036-4 Gompf,...
Marston; Baiada, Emilio (1953), "Homotopy and homology related to the Schoenfliesproblem", Annals of Mathematics, 2, 58: 142–165, doi:10.2307/1969825, MR 0056922...
family of functions where two critical points are destroyed. The PL-Schoenfliesproblem for S 2 ⊂ R 3 {\displaystyle S^{2}\subset \mathbb {R} ^{3}} was solved...
others, could be substituted, as Hilbert is reported to have said to Schoenflies and Kötter, by tables, chairs, glasses of beer and other such objects...
geometric topology. In an elementary fashion, he proved the generalized Schoenflies conjecture (his complete proof required an additional result by Marston...
theorem Coxeter group Crystallographic group Crystallographic point group, Schoenflies notation Discrete group Euclidean group Even and odd permutations Frieze...
kirstallographischen Resultate des Herrn Schoenflies und der meinigen" [Compilation of the crystallographic results of Mr. Schoenflies and of mine]. Zeitschrift für...
these 5 operations. The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions...
axiomatic method employed by second group composed of Zermelo, Fraenkel and Schoenflies, von Neumann worried that "We see only that the known modes of inference...
necessary condition for the existence of strong extrema of variational problems. He also helped devise the Weierstrass–Erdmann condition, which gives sufficient...
indicate the lattice angles, lattice parameters, Bravais lattices and Schöenflies notations for the respective lattice systems. In four dimensions, there...
Rotation by θ = 360°/n for any positive integer n is denoted Cn (from the Schoenflies notation for the group Cn that it generates). The identity operation...
decreasing sequence of cardinals. The equivalence was conjectured by Schoenflies in 1905. Abstract algebra Hahn embedding theorem: Every ordered abelian...
Vallée Poussin had already been critically analyzed and completed by Schoenflies (1924). Due to the importance of the Jordan curve theorem in low-dimensional...
structure has a point group 6 mm (Hermann–Mauguin notation) or C6v (Schoenflies notation), and the space group is P63mc or C6v4. The lattice constants...
indecomposable continuum that disproved a conjecture made by Arthur Moritz Schoenflies that, if X 1 {\displaystyle X_{1}} and X 2 {\displaystyle X_{2}} are...
the global average temperature. Fyodorov–Schoenflies theorem concluded by Yevgraf Fyodorov and Arthur Schoenflies from their work on crystallographic groups...
also equivalent to the axiom of choice. Writing in 1908, Arthur Moritz Schoenflies found in his report on set theory that the newer theory of ordered sets...
Sohncke's work) by a collaborative effort of Evgraf Fedorov and Arthur Schoenflies. 1895 – Wilhelm Conrad Röntgen discovers X-rays in experiments with electron...
other hand several important tools from topology including the Jordan–Schoenflies theorem are not proven, and that several related classification results...
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