On weakening tightness to weak tightness

  title={On weakening tightness to weak tightness},
  author={Angelo Bella and Nathan A. Carlson},
  journal={Monatshefte f{\"u}r Mathematik},
  • A. Bella, N. Carlson
  • Published 15 January 2019
  • Mathematics, Physics
  • Monatshefte für Mathematik
The weak tightness wt ( X ) of a space X was introduced in Carlson (Topol Appl 249:103–111, 2018 ) with the property $$wt(X)\le t(X)$$ w t ( X ) ≤ t ( X ) . We investigate several well-known results concerning t ( X ) and consider whether they extend to the weak tightness setting. First we give an example of a non-sequential compactum X such that $$wt(X)=\aleph _0<t(X)$$ w t ( X ) = ℵ 0 < t ( X ) under $$2^{\aleph _0}=2^{\aleph _1}$$ 2 ℵ 0 = 2 ℵ 1 . In particular, this demonstrates the… 
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