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)].
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