RT Journal Article
T1 On the uniform approximation of Cauchy continuous functions
A1 Beer, Gerald
A1 Garrido, M. Isabel
AB In the context of real-valued functions defined on metric spaces, it is known that the locally Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in the small functions - the locally Lipschitz functions where both the local Lipschitz constant and the size of the neighborhood can be chosen independent of the point - are uniformly dense in the uniformly continuous functions. Between these two basic classes of continuous functions lies the class of Cauchy continuous functions, i.e., the functions that map Cauchy sequences in the domain to Cauchy sequences in the target space. Here, we exhibit an intermediate class of Cauchy continuous locally Lipschitz functions that is uniformly dense in the real-valued Cauchy continuous functions. In fact, our result is valid when our target space is an arbitrary Banach space.
PB Elsevier Science
SN 0166-8641
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/24538
UL https://hdl.handle.net/20.500.14352/24538
LA eng
NO Ministerio de Economía y Competitividad (MINECO)
DS Docta Complutense
RD 21 abr 2025