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 
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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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