Quantum gravity as a theory of quantum spacetime

This article presents and discusses, from an epistemological point of view, a quantum theory of spacetime based on principles built from infinite mathematics applied to natural philosophy, cosmology and Riemannian geometry. A cautious argument shows that there is no logical reason to suppose that the ultimate structure of the universe is discontinuous from the moment that one considers an expanding universe. General relativity and quantum mechanics are evoked by discussing the barriers that today hinder a theory of great unification. A brief explanation of Lyra's geometry is made under the application of singularity functions in the context of the proposed theory. In addition, a quick appreciation of the current state of the investigations is made, showing the role of the proposed theory in the scenario of modern research.