A note on home-product-minimality

A compact space $Y$ is called homeo-product-minimal if given any minimal system $(X,T)$, it admits a homeomorphism $S:Y\to Y$, such that the product system $(X\times Y,T\times S)$ is minimal. We show that a large class of cofrontiers is homeo-product-minimal. This class contains R. H. Bing's pseudo-circle, answering a question of Dirb\'{a}k, Snoha and \v{S}pitalsk\'{y} from [Minimal direct products, Trans. Amer. Math. Soc. 375 (2022)].