On the uniform approximation of Cauchy continuous functions



Downloads per month over past year

Beer, Gerald and Garrido, M. Isabel (2016) On the uniform approximation of Cauchy continuous functions. Topology and its Applications, 208 (1). pp. 1-9. ISSN 0166-8641

[thumbnail of Garrido20.pdf] PDF
Restringido a Repository staff only


Official URL: http://www.sciencedirect.com/science/article/pii/S0166864116300578


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.

Item Type:Article
Uncontrolled Keywords:Cauchy continuous function; Cauchy-Lipschitz function; Lipschitz in the small function; Locally Lipschitz function; Primary; Secondary; Uniform approximation
Subjects:Sciences > Mathematics > Functions
ID Code:38178
Deposited On:23 Jun 2016 08:23
Last Modified:12 Dec 2018 15:12

Origin of downloads

Repository Staff Only: item control page