A note on condensations of function spaces onto σ-compact and analytic spaces

الأصل · EN

Modifying a construction of W. Marciszewski we prove (in ZFC) that there exists a subspace of the real line R, such that the realcompact space Cₚ(X) of continuous real-valued functions on X with the pointwise convergence topology does not admit a continuous bijection onto a σ-compact space. This answers a question of Arhangel'skii.