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

2013/12/20 by Mikołaj Krupski, Krupski, Mikołaj
Mathematics · #54A10 #54C35 #54D60 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54A10 #msc:54C35 #msc:54D60

paper · pdf · doi:10.48550/arxiv.1312.6081

arxiv created 2013/12/20 · arxiv updated 2013/12/23

Abstract

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 C_p(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.

Related

• Function spaces on separable compact lines
• Linear continuous surjections of C_p-spaces over compacta
• Function spaces on Corson-like compacta
• Compact condensations of Hausdorff spaces
• On the weak and pointwise topologies in function spaces