Cantor and generalized continuum hypotheses may be false

Cantor and generalized contunuum hypotheses are shown to be possibly factually false. Two new hyper-continuum hypotheses are posted to challenge pure mathematics and stir investigations of the abstract multispatial hyperspace, which is important for physical applications. Unlike the Cantorian hypotheses, however, the new ones conjecture existence of certain distinct, mixed kind of hyper-continuum that may serve as the manifold over which dual pairs of linear vector spaces with quite unrestricted abstract operations could be effectively constructed.