We observe the existence of a $\sigma$-compact, separable topological group $G$ and a countable topological group $H$ such that the tightness of $G$ is countable, but the tightness of $G\times H$ is equal to $\frak c$.
@article{118842,
author = {Oleg Okunev},
title = {A remark on the tightness of products},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {37},
year = {1996},
pages = {397-399},
zbl = {0854.54013},
mrnumber = {1399012},
language = {en},
url = {http://dml.mathdoc.fr/item/118842}
}
Okunev, Oleg. A remark on the tightness of products. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 397-399. http://gdmltest.u-ga.fr/item/118842/
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