Category:Definitions/Baire Category

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Baire Category.
Related results can be found in Category:Baire Category.


The Baire category of a topological space $T$ is a way of specifying how dense $T$ is:


First Category (Meager)

Let $T = \struct {S, \tau}$ be a topological space.

Let $A \subseteq S$.


$A$ is meager in $T$ if and only if it is a countable union of subsets of $S$ which are nowhere dense in $T$.


Second Category (Non-Meager)

$A$ is non-meager in $T$ if and only if it cannot be constructed as a countable union of subsets of $S$ which are nowhere dense in $T$.

That is, $A$ is non-meager in $T$ if and only if it is not meager in $T$.