examples of filters

  • If X is any set and AX then ={FX:AF} is a fixed filter on X; is an ultrafilterMathworldPlanetmath iff A consists of a single point.

  • If X is any infinite setMathworldPlanetmath, then {FX:XFis finite } is a free filter on X, called the cofinite filter.

  • The filter on generated by the filter base {(n,):n} is called the Fréchet filter on ; it is a free filter which does not convergePlanetmathPlanetmath or have any accumulation pointsMathworldPlanetmathPlanetmath.

  • The filter on generated by the filter base {(0,ε):ε>0} is a free filter on which converges to 0.

Title examples of filters
Canonical name ExamplesOfFilters
Date of creation 2013-03-22 12:54:31
Last modified on 2013-03-22 12:54:31
Owner Evandar (27)
Last modified by Evandar (27)
Numerical id 8
Author Evandar (27)
Entry type Example
Classification msc 54A99
Classification msc 03E99
Defines cofinite filter
Defines Fréchet filter