WebThis question may be formulated as a question of metrisable compactification of a real line, that is, of an injective map of R into a metrisable compact. The smallest such compactification is the ... WebIn the sequel G# will denote the group G equipped with the Bohr topol-ogy. The completion of G# is known as the Bohr compactification of G and 2000 Mathematics Subject Classification. Primary 05D10, 20K45; Secondary 22A05, 54H11. Key words and phrases. Bohr topology, homeomorphism, dimension, Ramsey theorem, partition theorem.
Is there any metric in which the set of real numbers R is compact ...
WebApr 16, 2008 · Download PDF Abstract: We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new … WebNov 13, 2024 · The spectrum of $\Cb(\mathbb R)$ is well known to be the Stone–Čech compactification $\beta (\mathbb R)$, ... So perhaps I should have emphasized that one should see the acting group as the discrete real line. I suppose one needs to consider the Bohr compactification if one wants a continuous action, right? ... no window in kitchen
end compactification in nLab
WebAug 4, 2010 · Bohr compactification of the real line. 29. Operator *-algebras and spectral theorem. 30. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID) 31. Basics of harmonic analysis on compact Lie groups. 32. Spin-network functions for SU(2) 33 + Functional analytic description of classical connection dynamics. References. … WebJan 5, 2004 · First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide … WebMay 1, 2024 · The Bohr compactification of , , is the -vector space of all real valued -linear functions on . (Equivalently, the set of all additive group homomorphisms from to … nicole eggert who played jamie powell