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Results tagged with order-theory
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user 11640
3
votes
Definition of continuous functions in order theory
They are not equivalent even for complete lattices. For example, consider the lattice (actually, frame) $\textrm{Ouv}(X)$ of open sets of a topological space $X$. Given a continuous map $f : X \to Y$, …
- 15.9k
9
votes
1
answer
366
views
Is an open map with open relative diagonal necessarily a local homeomorphism?
Let $f : X \to Y$ be an open (and continuous) map of locales. Suppose the relative diagonal $\Delta_f : X \to X \times_Y X$ is an open embedding of locales. Does it follow that $f : X \to Y$ is a loca …
- 15.9k
8
votes
Accepted
Posets (partially ordered sets) in equational logic
No. The category of models of an equational theory (i.e. a variety in the sense of universal algebra) is always a regular category, but the category of posets is not regular.
- 15.9k