User:Kompik/Math/Filter

Various definition of filter/ideal
In mathematical literature, various definitions of a filter/ideal can be found.

Filter defined with the condition $$\emptyset\notin\mathcal F$$: [B, p.57, Definition 1] [HH, p.74, Definition 9.1], [HJ, p.201, Definition 11.1], [J, Definition 7.1], [L, Definition 4.1]

Filter defined without the condition $$\emptyset\notin\mathcal F$$: [JW2, p.1], [C, p.60, Exercise 3]

Ideal defined with the condition $$X\notin\mathcal I$$: [HH, p.145, Definition 12.2], [HJ, p.202, Definition 11.1], [J, Definition 7.1], [L, Definition 4.1]

Ideal defined without the condition $$X\notin\mathcal I$$: [C, p.14], [JW2, p.2]