# Robert Bonnet: On hereditarily compact interval spaces

Shalom,
We will held seminar on Wednesday, December 14,
time 11:00-13:00, seminar room 201.
Speaker: Robert Bonnet (France)
Title: On hereditarily compact interval spaces

Abstract:
A compact interval space is a (complete) linear ordering $(L,<)$
such that a basis of the topology consists of the set of all open intervals of $L$. (For instance $[0,1]$ as subset of the real line is a compact interval space.)

We say that $X$ is a hereditarily compact interval space whenever every continuous image is a compact interval space (in particular $X$ is a compact interval space).

We shall prove that if $X$ is a hereditarily compact interval space,
then $X$ is homeomorphic to $alpha + 1$ where $alpha$ is a countable ordinal (and $alpha + 1$ is considered as compact interval space).