Advertisement

Abstract

In 2.1–2.2 X is a topological space, so, e.g., X may be a metric space, or, in particular, ℝN. A set AX is called nowhere dense iff int cl A = ⊘. A set AX is said to be of the first category iff A is a countable union of nowhere dense sets:
$$ A = \bigcup\limits_{i = 1}^\infty {A_i , int cl A_i } = \emptyset , i \in \mathbb{N}. $$
(2.1.1)

Keywords

Topological Space Regular System Countable Union Countable Base Complete Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag AG 2009

Personalised recommendations