Homeomorphisms of balls

Let $B^n = \{x \in \R^n \mid |x| \leq 1\}$$<wikitex>; Let $B^n = \{x \in \R^n \mid |x| \leq 1\}$ be the $n$-ball. Is every homeomoprhism of $B^n$ topologically isotopic to either the identity (orientation preserving case) or a reflection (orientation reversing case)? And does the answer depend on $n$? </wikitex> <!-- == References == {{#RefList:}} --> [[Category:Questions]] [[Category:Study questions]]B^n = \{x \in \R^n \mid |x| \leq 1\}$ be the $n/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_L4KhHp$$n$-ball. Is every homeomoprhism of $B^n$$B^n$ topologically isotopic to either the identity (orientation preserving case) or a reflection (orientation reversing case)?

And does the answer depend on $n$$n$?