Upper bounds for the tightness of the $G_\delta$-topology

DOI10.1007/S00605-020-01495-4arXiv1911.11461MaRDI QIDQ6329890

Publication date: 26 November 2019

Abstract: We prove that if

X

is a regular space with no uncountable free sequences, then the tightness of its

G_{d} e l t a

topology is at most continuum and if

X

is in addition Lindel"of then its

G_{d} e l t a

topology contains no free sequences of length larger then the continuum. We also show that the higher cardinal generalization of our theorem does not hold, by constructing a regular space with no free sequences of length larger than

o m e g a_{1}

, but whose

G_{d} e l t a

topology can have arbitrarily large tightness.

Mathematics Subject Classification ID

Sequential spaces (54D55) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25)

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