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On Uniformly Continuous Surjections Between Function Spaces

Ali Emre Eysen ⟨aemreeysen@hotmail.com⟩

Abstract:

Joint work with V. Valov

We consider uniformly continuous surjections between Cp(X) and Cp(Y) (resp, $C_p^(X)andC_p^(Y))andshowthatifXhassomedimensionallikeproperties,thensodoesY.Inparticular,weprovethatifT:C_p^(X)\to C_p^(Y)isacontinuouslinearsurjection,then\dim Y=0provided\dim X=0$. This provides a partial answer to a question raised by Kawamura-Leiderman.

Status: Accepted

Collection: Set-Theoretic Topology

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