Here are some prominent potential counterexamples to AC):
...with certain $2$-complexes of minimal Euler characteristic, eliminates any potential difference between simple-homotopy and $3$-deformations: A simple homotopy
31 KB (4,667 words) - 17:46, 1 July 2020
...these ideas the laws of Alexander duality and their generalization, [[knot theory]], were obtained.
...The fundamental tools for comparing triples are, in the spirit of category theory, continuous homomorphisms between them.
38 KB (5,626 words) - 17:15, 20 March 2018
$#C+1 = 407 : ~/encyclopedia/old_files/data/D031/D.0301380 Descriptive set theory
...ion, intersection, taking a complement or projection, etc. Descriptive set theory was created in the early 20th century by the studies of E. Borel, R. Baire
44 KB (6,667 words) - 11:40, 26 March 2023
$#C+1 = 270 : ~/encyclopedia/old_files/data/S086/S.0806530 Spectral theory of differential operators
The branch of the general [[Spectral theory|spectral theory]] of operators in which one investigates the spectral properties of differe
32 KB (4,393 words) - 08:22, 6 June 2020
...cation later in the research of N. Wiener (1923). The basis of the general theory of continuous-time Markov processes was laid by A.N. Kolmogorov .
In the theory of Markov processes most attention is given to homogeneous (in time) proces
27 KB (3,884 words) - 08:38, 21 January 2024
...t]" vs. "He saw [the man] [with a telescope]instrument" ). The ambiguity potential of syntactic structures like the attachment of prepositional or noun phrase
..., elementary sounds, which are represented as phonemes. While phonemes are abstract description units, the link to concrete speech is made in the field of phon
18 KB (2,627 words) - 17:03, 1 July 2020
...proceed without conservation of energy: in problems with friction, in the theory of open resonators, in problems of inelastic scattering, and others. Certai
...y of non-self-adjoint operators. Many of the propositions referring to the theory of non-self-adjoint operators are valid also for operators acting in arbitr
35 KB (5,059 words) - 04:12, 9 May 2022
$#C+1 = 144 : ~/encyclopedia/old_files/data/P072/P.0702430 Perturbation theory
...ysics, and technology. In this article the principal ideas of perturbation theory are given from a general point of view.
35 KB (5,181 words) - 07:24, 8 June 2020
...itional pure mathematics could be constructed rigorously starting from the theory of natural numbers.
* in set theory: Cantor and Dedekind
189 KB (29,059 words) - 14:31, 19 March 2023