Modifications of the double arrow space and related Banach spaces C(K)

Witold Marciszewski. "Modifications of the double arrow space and related Banach spaces C(K)." Studia Mathematica 184.3 (2008): 249-262. <http://eudml.org/doc/284590>.

@article{WitoldMarciszewski2008,
abstract = {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 ⊂ 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 $C(K_\{A\})$.},
author = {Witold Marciszewski},
journal = {Studia Mathematica},
keywords = { space; weak topology; separable linearly ordered compact space},
language = {eng},
number = {3},
pages = {249-262},
title = {Modifications of the double arrow space and related Banach spaces C(K)},
url = {http://eudml.org/doc/284590},
volume = {184},
year = {2008},
}

TY - JOUR
AU - Witold Marciszewski
TI - Modifications of the double arrow space and related Banach spaces C(K)
JO - Studia Mathematica
PY - 2008
VL - 184
IS - 3
SP - 249
EP - 262
AB - 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 ⊂ 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 $C(K_{A})$.
LA - eng
KW - space; weak topology; separable linearly ordered compact space
UR - http://eudml.org/doc/284590
ER -