Enflo, Per H.Gurariy, VladimirSeoane Sepúlveda, Juan Benigno2023-06-192023-06-1920140002-994710.1090/S0002-9947-2013-05747-9https://hdl.handle.net/20.500.14352/33431A subset M of a topological vector space X is called lineable (respectively, spaceable) in X if there exists an infinite dimensional linear space (respectively, an infinite dimensional closed linear space) Y subset of M boolean OR {0}. In this article we prove that, for every infinite dimensional closed subspace X of C[0, 1], the set of functions in X having infinitely many zeros in [0, 1] is spaceable in X. We discuss problems related to these concepts for certain subsets of some important classes of Banach spaces (such as C[0, 1] or Muntz spaces). We also propose several open questions in the field and study the properties of a new concept that we call the oscillating spectrum of subspaces of C[0, 1], as well as oscillating and annulling properties of subspaces of C[0, 1].engjournal articlehttp://www.ams.org/journals/tran/2014-366-02/S0002-9947-2013-05747-9/S0002-9947-2013-05747-9.pdfhttp://www.ams.org/restricted access517Lineabilityspaceabilitysubspaces of continuous functionszeros of functionsMuntz spacesAnálisis matemático1202 Análisis y Análisis Funcional