A note on the tightness of G_δ-modifications

2019/03/31 by Usuba, Toshimichi
#03E55 #54A25 #54C35 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1904.00322

Abstract

We construct a normal countably tight T₁ space X with t(X_δ) >2^ω. This is an answer to the question posed by Dow-Juhász-Soukup-Szentmiklóssy-Weiss. We also show that if the continuum is not so large, then the tightness of G_δ-modifications of countably tight spaces can be arbitrary large up to the least ω₁-strongly compact cardinal.

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