The simplest example is that of R n {\displaystyle \mathbb {R} ^{n}} . In this case the tangent bundle is trivial: each T x R n {\displaystyle T_{x}\mathbf {\mathbb {R} } ^{n}} is canonically isomorphic to T 0 R n {\displaystyle T_{0}\mathbb {R} ^{n}} via the map R n → R n {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} ^{n}} which subtracts x {\displaystyle x} , giving a diffeomorphism T R n → R n × R n {\displaystyle T\mathbb {R} ^{n}\to \mathbb {R} ^{n}\times \mathbb {R} ^{n}} .