English

Rational Extensions of C(X) via Hausdorff Continuous Functions

Rings and Algebras 2007-12-05 v1 Classical Analysis and ODEs

Abstract

The ring operations and the metric on C(X)C(X) are extended to the set Hnf(X)\mathbb{H}_{nf}(X) of all nearly finite Hausdorff continuous interval valued functions and it is shown that Hnf(X)\mathbb{H}_{nf}(X) is both rationally and topologically complete. Hence, the rings of quotients of C(X)C(X) as well as their metric completions are represented as rings of Hausdorff continuous functions.

Keywords

Cite

@article{arxiv.0712.0507,
  title  = {Rational Extensions of C(X) via Hausdorff Continuous Functions},
  author = {Roumen Anguelov},
  journal= {arXiv preprint arXiv:0712.0507},
  year   = {2007}
}
R2 v1 2026-06-21T09:50:15.451Z