Currently studying an article of Koji SEKIGUCHI "Ringed Spaces of Valuation Rings and Projective Limits of Schemes" from projecteuclid.org and the author gave in proposition 1 an equivalence:
The following two conditions for a local ringed space (X, $\mathcal{O}_{X}$ ) and a field $k$ are equivalent:
wjere the author talks about an injection between $\mathcal{O}_{X}(V)$ and Map(V,K) whitout mention of the map, so it seems like there is a canonical map.
What does the author mean here?