A compact space K is Corson compact if and only if Cp(K) has a dense lc-scattered subspace

We establish that a compact space K is Corson compact if and only if it can be embedded in a topological group which is a W-space in the sense of Gruenhage. As a application of this result we show that K is Corson compact if and only if it embeds in Cp(X) for a Lindel & ouml;f scattered space X. We also prove that a zero-dimensional compact space K is Corson if and only if Cp(K, {0, 1}) is a continuous image of a Lindel & ouml;f scattered space. Besides, a zero-dimensional countably compact space Xis omega-monolithic if and only if Cp(X) has a dense functionally countable subspace. (c) 2023 Elsevier Inc. All rights reserved.