A note on linearly ordered net spaces

James Robert Boone

Vol. 98 (1982), No. 1, 25–35

DOI: 10.2140/pjm.1982.98.25

Abstract

The linearly ordered net spaces are introduced in this paper. This concept is a generalization of both the sequential spaces and the linearly ordered base spaces. The fundamental properties of this class, including mapping properties, are presented. Various applications of a general nature are given as well as some applications to weak covering axioms. The class of lo-net spaces is characterized as the class of well-ordered net spaces.

Mathematical Subject Classification 2000

Primary: 54F05

Secondary: 06F99, 54D55

Milestones

Received: 3 September 1980

Revised: 6 January 1981

Published: 1 January 1982