Tricki
a repository of mathematical know-how

Cardinality, measure and category

Quick description

It is often useful to know that a set is small, or, even better, that every set of a certain type is small. The main property one looks for in a useful notion of smallness is that a union of many small sets is still small. Examples of notions of smallness are having few elements, being countable, being of measure zero, and being of the first category. This page contains links to articles on the general theme of smallness and how to exploit it.

A good way of proving that a set is countable

A quick way of recognising countable sets

How to change "for all x there exists y" into "there exists y such that for all x"

How to use the Baire category theorem