Abstract
Let X=∏α∈ω1Xα be a product of ω1 many separable metric spaces. It is proved that every C⁎-embedded subset in X is C-embedded in X under a certain set-theoretic assumption. Combining a result of E. Pol and R. Pol for N2ω, it is undecidable in ZFC that there is a (closed) C⁎-embedded but not C-embedded subset in Nω1. It is also proved in ZFC that every C-embedded subset in X is P-embedded in X. Next, we discuss when C⁎- or C-embedding implies P-embedding in products of generalized metrizable spaces, such as M-spaces, Σ-spaces and semi-stratifiable spaces.
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