The aim of this paper is to give a unifying description of various constructions of sites (subanalytic, semialgebraic, o-minimal) and consider the corresponding theory of sheaves. The method used applies to a more general context and gives new results in semialgebraic and o-minimal sheaf theory.
Mário J. EDMUNDO. Luca PRELLI. "Sheaves on $\mathcal T$-topologies." J. Math. Soc. Japan 68 (1) 347 - 381, January, 2016. https://doi.org/10.2969/jmsj/06810347