It is possible to define continuity over $\mathbb{Q},$ so it is possible to define a homeomorphism over $\mathbb{Q}.$ However, I don't see how we can define "closed" and "open" manifolds over $\mathbb{Q}$ (Qanifolds). My best definition is that a closed Qanifold is a Qanifold that can be extended to a closed manifold over $\mathbb{R},$ and an open Qanifold is a Qanifold that can be extended to an open manifold over $\mathbb{R}.$ Are there any Qanifolds that are both closed and open?
2026-04-12 07:10:44.1775977844
Definition of closed and open "Qanifolds" (manifolds over $\mathbb{Q}$): can a Qanifold be both closed and open?
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