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Fix-point free affine transformations having invariant lines. (English) Zbl 1289.51022
Summary: We extend a result of E. Kasparek [Ann. Math. Sil. 24(2010), 35–37 (2011; Zbl 1229.51025)] characterizing continuous affine transformations without fixed points $$f : X \to X$$ having invariant straight line to the case when $$X$$ is an arbitrary real topological linear space.
##### MSC:
 51N20 Euclidean analytic geometry
##### Keywords:
affine transformations; invariant lines; function equations
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