García-Pacheco, F.J.Martín Conde, MaríaSeoane Sepúlveda, Juan Benigno2023-06-202023-06-2020091027-5487https://hdl.handle.net/20.500.14352/50457We 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.engjournal articlehttp://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/463/349http://tjm.math.ntu.edu.tw/open access517.98Riemann integrableLebesgue integrableContinuous unbounded functionsAnálisis funcional y teoría de operadores