query: Any vector bundle on $\mathbb R$ is a trivial bundle
positive_passages.docid: 12772
positive_passages.text: A fiber bundle over Euclidean space is trivial.
negative_passages.docid: 47015
negative_passages.text: Vector Space Structures over ($\mathbb{R}$,+)
negative_passages.docid: 112548
negative_passages.text: Existence of non-trivial linear functional on any vector space
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$
negative_passages.docid: 110654
negative_passages.text: Vector Spaces and AC
negative_passages.docid: 7813
negative_passages.text: In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
negative_passages.docid: 148111
negative_passages.text: Every $R$-module is projective if and only if every $R$-module is injective
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 48419
negative_passages.text: Difference between $\mathbb{R}$-linear and $\mathbb{C}$-linear maps
negative_passages.docid: 52596
negative_passages.text: A basis for $k(X)$ regarded as a vector space over $k$
negative_passages.docid: 140962
negative_passages.text: Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
negative_passages.docid: 92504
negative_passages.text: Criteria of a trivial G bundle of a 3-manifold
negative_passages.docid: 149593
negative_passages.text: Global sections of a tensor product of vector bundles on a smooth manifold
negative_passages.docid: 6101
negative_passages.text: Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?
negative_passages.docid: 51786
negative_passages.text: Is every additive monofunctor between abelian categories left exact?
negative_passages.docid: 69893
negative_passages.text: An inner product space and its proper closed subspace with trivial orthogonal complement
negative_passages.docid: 39094
negative_passages.text: Lie bracket of vector fields on $\Bbb R^{n}$