%0 Journal Article
%T Vector bundles on real algebraic curves
%A Maciejewski, Łukasz
%J Universitatis Iagellonicae Acta Mathematica
%V 2012
%R 10.4467/20843828AM.12.003.1123
%N Tom 50
%P 63-68
%K Real algebraic curve, algebraic vector bundle, approximation of continuous maps by regular maps
%@ 0083-4386
%D 2012
%U https://ejournals.eu/czasopismo/universitatis-iagellonicae-acta-mathematica/artykul/vector-bundles-on-real-algebraic-curves
%X We prove that any topological real line bundle on a compact real algebraic curve X is isomorphic to an algebraic line bundle. The result is then generalized to vector bundles of an arbitrary constant rank. As a consequence we prove that any continuous map from X into a real Grassmannian can be approximated by regular maps.