A note on the tightness of Gδ-modifications

Toshimichi Usuba

doi:10.1016/j.topol.2019.106820

A note on the tightness of G_δ-modifications

Toshimichi Usuba

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 [5]. 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.

Original language	English
Article number	106820
Journal	Topology and its Applications
Volume	265
DOIs	https://doi.org/10.1016/j.topol.2019.106820
Publication status	Published - 2019 Sep 15

Keywords

Countably tight
G-modification
Saturated filter
ω-strongly compact cardinal

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1016/j.topol.2019.106820

Cite this

@article{071b9bddc977479395e073501a0328c6,

title = "A note on the tightness of Gδ-modifications",

abstract = "We construct a normal countably tight T1 space X with t(Xδ)>2ω. This is an answer to the question posed by Dow-Juh{\'a}sz-Soukup-Szentmikl{\'o}ssy-Weiss [5]. We also show that if the continuum is not so large, then the tightness of Gδ-modifications of countably tight spaces can be arbitrary large up to the least ω1-strongly compact cardinal.",

keywords = "Countably tight, G-modification, Saturated filter, ω-strongly compact cardinal",

author = "Toshimichi Usuba",

note = "Funding Information: This research was supported by JSPS KAKENHI Grant Nos. 18K03403 and 18K03404 . Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = sep,

day = "15",

doi = "10.1016/j.topol.2019.106820",

language = "English",

volume = "265",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier",

}

TY - JOUR

T1 - A note on the tightness of Gδ-modifications

AU - Usuba, Toshimichi

PY - 2019/9/15

Y1 - 2019/9/15

N2 - We construct a normal countably tight T1 space X with t(Xδ)>2ω. This is an answer to the question posed by Dow-Juhász-Soukup-Szentmiklóssy-Weiss [5]. We also show that if the continuum is not so large, then the tightness of Gδ-modifications of countably tight spaces can be arbitrary large up to the least ω1-strongly compact cardinal.

AB - We construct a normal countably tight T1 space X with t(Xδ)>2ω. This is an answer to the question posed by Dow-Juhász-Soukup-Szentmiklóssy-Weiss [5]. We also show that if the continuum is not so large, then the tightness of Gδ-modifications of countably tight spaces can be arbitrary large up to the least ω1-strongly compact cardinal.

KW - Countably tight

KW - G-modification

KW - Saturated filter

KW - ω-strongly compact cardinal

UR - http://www.scopus.com/inward/record.url?scp=85069600859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069600859&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2019.106820

DO - 10.1016/j.topol.2019.106820

M3 - Article

AN - SCOPUS:85069600859

VL - 265

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

M1 - 106820

ER -