Lineability, spaceability, and algebrability of certain subsets of function spaces.

We construct infinite-dimensional Banach spaces and infinitely generated Banach algebras of functions that, except for 0, satisfy some kind of special or pathological property. Three of these structures are: a Banach algebra of everywhere continuous bounded functions which are not Riemann-integrable; a Banach space of Lebesgue-integrable functions that are not Riemann-integrable; an algebra of continuous unbounded functions defined on an arbitrary non-compact metric space. ; MEC ; MEC ; Depto. de Análisis Matemático y Matemática Aplicada ; Fac. de Ciencias Matemáticas ; Instituto de Matemática Interdisciplinar (IMI) ; TRUE ; pub