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A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of an abelian compact topological group. Solenoids were first introduced by Vietoris for the n i = 2 {\displaystyle n_{i}=2} case, [ 2 ] and by van Dantzig the n i = n {\displaystyle n_{i}=n} case, where n ≥ 2 {\displaystyle n\geq 2} is fixed. [ 3 ]
An infinite solenoid has infinite length but finite diameter. "Continuous" means that the solenoid is not formed by discrete finite-width coils but by many infinitely thin coils with no space between them; in this abstraction, the solenoid is often viewed as a cylindrical sheet of conductive material.
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. [1] The concept was introduced by Zermelo in the 1930s. [2]Some infinitary logics may have different properties from those of standard first-order logic.
If an NL-complete language X could belong to L, then so would every other language Y in NL.For, suppose (by NL-completeness) that there existed a deterministic logspace reduction r that maps an instance y of problem Y to an instance x of problem X, and also (by the assumption that X is in L) that there exists a deterministic logspace algorithm A for solving problem X.
Then the formal language Pref(w) contains every finite prefix of w. Limit Given a finite-length language L, an ω-word w is in the limit of L if and only if Pref(w) ∩ L is an infinite set. In other words, for an arbitrarily large natural number n, it is always possible to choose some word in L, whose length is greater than n, and which is a ...
A U.S. military appeals court has ruled that plea deals related to the man accused of masterminding the Sept. 11, 2001, attacks and two accomplices can proceed after Defense Secretary Lloyd Austin ...
Given a point A 0 in a Euclidean space and a translation S, define the point A i to be the point obtained from i applications of the translation S to A 0, so A i = S i (A 0).The set of vertices A i with i any integer, together with edges connecting adjacent vertices, is a sequence of equal-length segments of a line, and is called the regular apeirogon as defined by H. S. M. Coxeter.
Last night, the actor defied the cold weather in New York City, stepping out in a pair of black leather micro shorts.