Definition:Continuous Map (Locale)
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Definition
Let $\mathbf{Loc}$ denote the category of locales.
A morphism of $\mathbf{Loc}$ is called a continuous map.
That is, for locales $L_1 = \struct{S_1, \preceq_1}$ and $L_2 = \struct{S_2, \preceq_2}$:
- $\phi: L_1 \to L_2$ is a continuous map:
- $\phi$ is a frame homomorphism $\phi: L_2 \to L_1$
Also see
Sources
- 1982: Peter T. Johnstone: Stone Spaces: Chapter II: Introduction to Locales, $\S1.1$ Definition (b)