Category:Baire Category
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This category contains results about Baire Category.
Definitions specific to this category can be found in Definitions/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 $T$.
Subcategories
This category has the following 2 subcategories, out of 2 total.