Nature

Helmholtz on the Axioms of Geometry

THE Academy journal of the 12th of February, 1870 (vol. i. p. 128), contained a paper by Prof. Helmholtz upon the Axioms of Geometry in a philosophical point of view. The opinions set forth by him ...
JSTOR Daily

Connections between Axioms of Set Theory and Basic Theorems of Universal Algebra

One of the basic theorems in universal algebra is Birkhoff's variety theorem: the smallest equationally axiomatizable class containing a class K of algebras coincides with the class obtained by taking ...
Nature

On the Simplest Continuous ManiFoldness of Two Dimensions and of Finite Extent 1

ONE of the most remarkable speculations of the present century is the speculation that the axioms of geometry may be only approximately true, and that the actual properties of space may be somewhat ...
JSTOR Daily

Modulus of Families of Sets of Finite Perimeter and Quasiconformal Maps Between Metric Spaces of Globally Q-bounded Geometry

We generalize a result of Kelly [17] to the setting of Ahlfors Q-regular metric measure spaces supporting a 1-Poincaré inequality. It is shown that if X and Y are two Ahlfors Q-regular spaces ...