nLab sigma-frame

Contents

Contents

Definition

A σ\sigma-frame is a σ \sigma -complete lattice (L,,,,,,)(L, \leq, \bot, \vee, \top, \wedge, \Vee) such that for all elements aLa \in L and sequences s:Ls:\mathbb{N} \to L,

a n:s(n)= n:as(n)a \wedge \Vee_{n:\mathbb{N}} s(n) = \Vee_{n:\mathbb{N}} a \wedge s(n)

Examples

  • Sierpinski space, denoted as Σ\Sigma or 1 1_\bot, is the initial σ\sigma-frame.

See also

References

Last revised on May 12, 2022 at 09:05:14. See the history of this page for a list of all contributions to it.