Geodesic
Tightness of compact spaces is preserved by the $t$-equivalence relation
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 335-342

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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.
Classification : 46E10, 54A10, 54A25, 54B05, 54B10, 54C35, 54C60, 54D20, 54D30, 54D55
Keywords: function spaces; topology of pointwise convergence; tightness 
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     author = {Okunev, Oleg},
     title = {Tightness of compact spaces is preserved by the $t$-equivalence relation},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {335--342},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2002},
     mrnumber = {1922131},
     zbl = {1090.54004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a10/}
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Okunev, Oleg. Tightness of compact spaces is preserved by the $t$-equivalence relation. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 335-342. http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a10/