The Lindelöf property is \(1\)-invariant
The main role in \(C_p\)-theory is played by the topological ring \(C_p(X)\) formed by all continuous real valued functions on a space \(X\) in the topology of pointwise convergence. A general question on \(C_p\)-theory is: when are \(C_p(X)\) and \(C_p(Y)\) linearly homeomorphic as linear topological spaces. We say that spaces \(X\) and \(Y\) are \(l\)-equivalent if \(C_p(X)\) and \(C_p(Y)\) are linearly homeomorphic. The topological properties preserved by the relation of \(l\)-equivalence are called \(l\)-invariant. In [Topological function spaces (1992; Zbl 0758.46026)] \textit{A. V. Arkhangel'skij} posed whether the Lindelöf property is \(l\)-invariant. In this paper Arkhangel'skij's question is solved.
scientific article; zbMATH DE number 1307923