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Around tight points

✍ Scribed by A. Bella; V.I. Malykhin

Book ID
104295289
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
557 KB
Volume
87
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

We present three examples of countable spaces with a single nonisolated point. The first gives, assuming CH, a FrCchet-Urysohn tight point which does not have countable absolute tightness; the second, constructed with the help of o, gives a tight non-weakly Frkchet-Urysohn point without countable absolute tightness; the third gives a weakly Frbchet-Urysohn point which is not Frechet-Urysohn, has countable fan-tightness but is not tight.

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The countable spaces whose product with the sequential fan S, have countable tightness are characterized. As a consequence. it is shown that if ?l x S, has countable tightness then X has countable fan-tightness.

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