Modifications of the double arrow space and related Banach spaces $C(K)$
Tom 184 / 2008
Studia Mathematica 184 (2008), 249-262 MSC: Primary 46B03, 46E15, 54C35, 54F05. DOI: 10.4064/sm184-3-4
We consider the class of compact spaces $K_A$ which are modifications of the well known double arrow space. The space $K_A$ is obtained from a closed subset $K$ of the unit interval $[0,1]$ by “splitting” points from a subset $A\subset K$. The class of all such spaces coincides with the class of separable linearly ordered compact spaces. We prove some results on the topological classification of $K_A$ spaces and on the isomorphic classification of the Banach spaces $C(K_A)$.