Abstract: In a linearly ordered topological space (LOTS), -points, -points and naturally -space and -space are defined and an example of a -space without -points, which is also an example of a LOTS almost P-space
without P-points is given. Using these concepts, we show that in the
category of linearly ordered topological spaces, quasi F-spaces and almost P-spaces
coincide. We also show that a LOTS is sequentially disconnected if and only if
it is either disconnected or it has at least one almost P-point.
Keywords and phrases: almost P-point,
quasi F-space, -space, sequential space, sequentially connected space,
tightness.