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shrinking space

Open Moniker1998 opened this issue 1 year ago • 2 comments

https://en.wikipedia.org/wiki/Shrinking_space

A property for which it would be nice to have examples for.

Implies: normal, countably paracompact

Implied by: normal metacompact

Moniker1998 avatar Jul 18 '24 19:07 Moniker1998

A couple of things to consider about the shrinking property for additional reference:

  • According to https://zbmath.org/0712.54016, a submetacompact space is shrinking iff it is normal. Do we want to add in submetacompact to the pi-base as well?
  • Are there well-known examples that separate shrinking from the other related properties outlined in the issue? It may be useful to have these in hand to add in with the PR adding in the shrinking property.

ccaruvana avatar Aug 15 '24 20:08 ccaruvana

Submetacompactness (= $\theta$-refinable) seems to be a well-studied property with important connections to other properties. See for example http://topology.nipissingu.ca/tp/reprints/v03/tp03207s.pdf. Worth having in pi-base.

prabau avatar Aug 20 '24 05:08 prabau