Call a space X (weakly) Japanese at a point x∈X if X has a closure-preserving local base (or quasi-base respectively) at the point x. The space X is (weakly) Japanese if it is (weakly) Japanese at every x∈X. We prove, in particular, that any generalized ordered space is Japanese and that the property of being (weakly) Japanese is preserved by σ-products; besides, a dyadic compact space is weakly J
![A glance at spaces with closure-preserving local bases](https://cdn-ak-scissors.b.st-hatena.com/image/square/b59e2a97f037f55711b4e51f72e1dc31aa2337a2/height=288;version=1;width=512/https%3A%2F%2Fars.els-cdn.com%2Fcontent%2Fimage%2F1-s2.0-S0166864109X00192-cov150h.gif)