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The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.

2 votes

Proper coverings as a quotient of the coverings

I don't think they are isomorphic. Let $X=\mathbb N$ and let $A$ be a covering consisting of the sets of the form $$ a_n = \{ 0, \dots, n \} $$ for every $n\in \mathbb N$. Then, $A$ is not $\simeq$-e …
Tomáš Jakl's user avatar