Talk:Microbundles (Ex)

Definition 0.1.

An $<wikitex>; Let us begin with the definition of microbundle. {{beginthm|Definition|}} An $n$-dimensional microbundle is a quadruple $(E,B,i,j)$ such that there is a sequence $$B\xrightarrow{i} E\xrightarrow{j} B$$ and the following conditions hold. *$j\circ i=\id_B$ *for all $x\in B$ there exist open neigbourhood $U\subset B$ and an open neighbourhood $V\subset E$ of $i(b)$ and a homeomorphism $$h\colon V\to U\times \mathbb{R}^n.$$ {{endthm}} </wikitex>n$-dimensional microbundle is a quadruple $(E,B,i,j)$ such that there is a sequence and the following conditions hold.

• $j\circ i=\id_B$
• for all $x\in B$ there exist open neigbourhood $U\subset B$ and an open neighbourhood $V\subset E$ of $i(b)$ and a homeomorphism
  $$\displaystyle h\colon V\to U\times \mathbb{R}^n.$$