International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 451-472
doi:10.1155/S016117128100032X

The star compactification

G. D. Richardson1 and D. C. Kent2

1Department of Mathematics, East Carolina University, Greenville 27834, N. C., USA
2Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USA

Received 18 September 1980

Copyright © 1981 G. D. Richardson and D. C. Kent. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The relationships between a convergence space and its star compactification is studied. Special attention is given to lifting properties of this compactification. In particular, it is shown that a natural extension of any continuous function to the respective compactification spaces is θ-continuous.