Geodesic
On some properties of quotients of homogeneous C(K) spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 1, pp. 33-43

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We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic to the space C([0,1]), then the quotient space X/Y contains a subspace isomorphic to the space C(K).
Keywords: nonseparable C(K) spaces, quotients of C(K) spaces 
Michalak, Artur. On some properties of quotients of homogeneous C(K) spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 1, pp. 33-43. http://geodesic.mathdoc.fr/item/DMDICO_2016_36_1_a1/
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