6533b86cfe1ef96bd12c8103
RESEARCH PRODUCT
Upper bounds for the tightness of the $$G_\delta $$-topology
Santi SpadaroAngelo Bellasubject
Delta010505 oceanographyContinuum (topology)GeneralizationGeneral Mathematics010102 general mathematicsFree sequenceTopologyLindelöf01 natural sciencesOmegaArbitrarily largeGdelta-topologyRegular spaceUncountable set0101 mathematicsTopology (chemistry)Tightness0105 earth and related environmental sciencesMathematicsdescription
We prove that if X is a regular space with no uncountable free sequences, then the tightness of its $$G_\delta $$ topology is at most the continuum and if X is, in addition, assumed to be Lindelof then its $$G_\delta $$ topology contains no free sequences of length larger then the continuum. We also show that, surprisingly, the higher cardinal generalization of our theorem does not hold, by constructing a regular space with no free sequences of length larger than $$\omega _1$$ , but whose $$G_\delta $$ topology can have arbitrarily large tightness.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-02-04 | Monatshefte für Mathematik |