Cleavability over scattered first-countable LOTS
linearly ordered topological space (LOTS)
A space \(X\) is \textit{cleavable} over a space \(Y\) \textit{along} \(A\subseteq X\) if there exists a continuous \(f: X\to Y\) such that \(f(A)\cap f(X\smallsetminus A)=\emptyset\). A space \(X\) is \textit{cleavable over} \(Y\) if it is cleavable over \(Y\) along all \(A\subseteq X\).NEWLINENEWLINEIn the present paper, the author examines cleavability over scattered first-countable LOTS, specifically cleavability over \(\omega_1\), answering some questions of \textit{A. V. Arhangel'skiĭ} [Ann. N. Y. Acad. Sci. 659, 18--28 (1992; Zbl 1250.54004)]. The main result asserts that if \(X\) is an infinite compactum cleavable over an infinite first-countable scattered LOTS, then \(X\) must be homeomorphic to a countable ordinal, and must also therefore be a LOTS.
scientific article; zbMATH DE number 6084117