## Oleg Okunev

*Tightness of compact spaces is preserved by the $t$-equivalence relation *

Comment.Math.Univ.Carolinae 43,2 (2002) 335-342. **Abstract:**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.

**Keywords:** function spaces, topology of pointwise convergence, tightness

**AMS Subject Classification:** 54B10, 54D20, 54A25, 54D55

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