Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658691 | Topology and its Applications | 2014 | 9 Pages |
Abstract
In this article, using the characterization of almost P-points of a linearly ordered topological space (LOTS) in terms of sequences, we observe that in the category of linearly ordered topological spaces, quasi F-spaces and almost P-spaces coincide. This coincidence gives examples of quasi F-spaces with no F-points. We also use the characterization of sequentially connected LOTS in terms of almost P-points to show that whenever each LOTS Xn has first and last elements, the lexicographic product ân=1âXn is sequentially connected if and only if each Xn is. Whenever each Xn is a LOTS without first and last elements, then it is shown that ân=1âXn is always a sequential space. The lexicographic product âα<Ï1Xα, where Ï1 is the first uncountable ordinal, is also investigated and it is shown that if each Xα contains at least two points, then âα<Ï1Xα is always an almost P-space (a quasi F-space) but it is neither sequential nor sequentially connected. Using this lexicographic product, we give an example of a quasi F-space in which the set of F-points and the set of non-F-points are dense. Whenever each Xα, α<Ï1, does not have first and last elements, we show that the lexicographic product âα<Ï1Xα is a P-space without isolated points.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
F. Azarpanah, M. Etebar,