# Talk:Microbundles (Ex)

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Let us begin with the definition of microbundle.

Definition 0.1.

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