# Equivalence Classes

### Some articles on equivalence, equivalence classes:

Admissible Representation - Real or Complex Reductive Lie Groups
... this notion is different than the usual equivalence, it is an important result that the two notions of equivalence agree for unitary (admissible) representations ... This reduces the study of the equivalence classes of irreducible unitary representations of G to the study of infinitesimal equivalence classes of admissible representations and the ... of parameterizing the infinitesimal equivalence classes of admissible representations was fully solved by Robert Langlands and is called the Langlands classification ...
Rough Set - Definitions - Attribute Dependency
... Each attribute set induces an (indiscernibility) equivalence class structure, the equivalence classes induced by given by, and the equivalence classes induced ... Let, where is a given equivalence class from the equivalence-class structure induced by attribute set ... set on attribute set, is given by That is, for each equivalence class in, we add up the size of its lower approximation by the attributes in, i.e ...
BRST Quantization - Gauge Transformations in QFT
... promising gauge theories, in which the objects in the theory represent equivalence classes of physically indistinguishable field configurations, any two of which are related ... fields contains many redundant degrees of freedom the distinct configurations of the theory are equivalence classes of field configurations, so that two descriptions which are ... but in a quotient space (or cohomology) whose elements are equivalence classes of field configurations ...
Topological Indistinguishability - Properties - Equivalence Classes
... To discuss the equivalence class of x, it is convenient to first define the upper and lower sets of x ... intersection of the neighborhood system at x The equivalence class of x is then given by the intersection Since ↓x is the intersection of all the closed sets containing x and ↑x is the ... Both cl{x} and ∩Nx will contain the equivalence class ...

### Famous quotes containing the word classes:

Of all reformers Mr. Sentiment is the most powerful. It is incredible the number of evil practices he has put down: it is to be feared he will soon lack subjects, and that when he has made the working classes comfortable, and got bitter beer into proper-sized pint bottles, there will be nothing left for him to do.
Anthony Trollope (1815–1882)