In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named after Andrey Nikolayevich Tikhonov (whose surname sometimes is transcribed Tychonoff), who proved it first in 1930 for powers of … See more The theorem depends crucially upon the precise definitions of compactness and of the product topology; in fact, Tychonoff's 1935 paper defines the product topology for the first time. Conversely, part of its importance is to … See more All of the above proofs use the axiom of choice (AC) in some way. For instance, the third proof uses that every filter is contained in an … See more • Alexander's sub-base theorem – Collection of subsets that generate a topology • Compactness theorem See more • Tychonoff's theorem at ProofWiki • Mizar system proof: See more Tychonoff's theorem has been used to prove many other mathematical theorems. These include theorems about compactness of … See more 1) Tychonoff's 1930 proof used the concept of a complete accumulation point. 2) The theorem is a quick corollary of the Alexander subbase theorem. More modern proofs … See more To prove that Tychonoff's theorem in its general version implies the axiom of choice, we establish that every infinite cartesian product of non-empty sets is nonempty. The … See more Web吉洪諾夫定理 (Tychonoff theorem)是關於緊空間的一條定理。. 該定理斷言:任意多個緊空間的積空間是緊空間.這個定理是有關緊性的最有用的定理，也是一般拓撲學中最重要的定 …
Tychonoff定理及其应用--《河南大学学报(自然科学版)》1997年04期
Web索伯列夫嵌入定理(Sobolev imbedding theorems)是索伯列夫空间最重要的性质，可以用索伯列夫不等式证明该定理。 WebTHE TYCHONOFF THEOREM1 The Tychonoff theorem asserts that the product of an arbitrary number of compact spaces is compact in the product topology. In Lecture Three … stephen fry snake in the trouser radio bit
Tychonoff定理和乘积拓扑 - 豆丁网
WebJan 14, 2024 · For a finite number of factors the proof of this statement is elementary (see below), but this already essentially implies for instance the Heine-Borel theorem.For an … WebMay 25, 2015 · 纳什嵌入定理((Nash Embedding Theorem)纳什嵌入定理是指以约翰·福布斯·纳什命名，指出每个黎曼流形可以等距嵌入到欧几里得空间R^n。“等距”表示“保持曲线长 … http://matheron.perso.math.cnrs.fr/recherche_fichiers/Tychonoff.pdf stephen fry president of mind