202412081812

Tags : Topology, Topology via Logic

Topological Spaces as Frames

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Let $X$ bet a set, and let $A$ be any subframe of $\mathcal{P}(A)$. i.e Any family of subsets of $X$ that:

• Contain the empty set and $X$
• Are closed under arbitrary union
• Are closed under finite intersection

This exactly happens to be the definition of a Topology, where the elements of $A$ happen to be the open subsets of $X$.

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References

Frames(Algebra)