Article
MSC:
46E10,
54A10,
54A25,
54B05,
54B10,
54C35,
54C60,
54D20,
54D30,
54D55 | MR 1922131 | Zbl 1090.54004
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Keywords:
function spaces; topology of pointwise convergence; tightness
function spaces; topology of pointwise convergence; tightness
Summary:
We prove that if there is an open mapping from a subspace of $C_p(X)$ onto $C_p(Y)$, then $Y$ is a countable union of images of closed subspaces of finite powers of $X$ under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if $X$ and $Y$ are $t$-equivalent compact spaces, then $X$ and $Y$ have the same tightness, and that, assuming $2^{\frak t}>\frak c$, if $X$ and $Y$ are $t$-equivalent compact spaces and $X$ is sequential, then $Y$ is sequential.
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