"On complemented copies of $c_0$ in spaces of vector-valued continuous functions with the pointwise topology."Bargetz, ChristianLet $X$ be a Tychonoff space and $E$ be a locally convex space. We denote by $C_p(X,E)$ the space of all continuous functions $X\to E$ equipped with the topology of pointwise convergence. In this talk, we discuss the question of when the space $C_p(X,E)$ contains a complemented copy of the space $c_0$ equipped with the pointwise topology, i.e. the topology induced by the countable product $\mathbb{R}^{\omega}$. Moreover we discuss the Josefson-Nissenzweig property of these spaces. This is joint work with Damian Sobota and Jerzy Kakol. |
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