Tightness of compact spaces is preserved by the $t$-equivalence relation
Okunev, Oleg
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 335-342 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2002-01-01
Classification:  46E10,  54A10,  54A25,  54B05,  54B10,  54C35,  54C60,  54D20,  54D30,  54D55 
@article{119323,
     author = {Oleg Okunev},
     title = {Tightness of compact spaces is preserved by the $t$-equivalence relation},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {335-342},
     zbl = {1090.54004},
     mrnumber = {1922131},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119323}
}

Okunev, Oleg. Tightness of compact spaces is preserved by the $t$-equivalence relation. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 335-342. http://gdmltest.u-ga.fr/item/119323/

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