query: Prove that every linear map on a finite dimensional vector space is continuous
positive_passages.docid: 45252
positive_passages.text: "Every linear mapping on a finite dimensional space is continuous"
negative_passages.docid: 83461
negative_passages.text: Continuous iff composition with every linear functional is continuous
negative_passages.docid: 152325
negative_passages.text: Every subspace of the dual of a finite-dimensional vector space is an annihilator
negative_passages.docid: 81471
negative_passages.text: Finite dimensional spaces
negative_passages.docid: 83046
negative_passages.text: A linear map, continuous at zero, is bounded
negative_passages.docid: 34700
negative_passages.text: Proving that the matrix exponential map is surjective onto the general linear group
negative_passages.docid: 29582
negative_passages.text: Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
negative_passages.docid: 59133
negative_passages.text: Show that an inverse of a bijective linear map is a linear map.
negative_passages.docid: 31747
negative_passages.text: Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space
negative_passages.docid: 54222
negative_passages.text: Prove the map has a fixed point
negative_passages.docid: 72044
negative_passages.text: prove $x \mapsto x^2$ is continuous
negative_passages.docid: 149999
negative_passages.text: fixed point of a continuous map on a projective space
negative_passages.docid: 112024
negative_passages.text: Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 65472
negative_passages.text: From injective map to continuous map
negative_passages.docid: 27478
negative_passages.text: Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
negative_passages.docid: 38033
negative_passages.text: A surjective linear map into a finite dimensional space is open