Finsler Structures onA-Bundles

Papatriantafillou, Makia H.

doi:10.1002/mana.19871300106

Cited by 4 publications

(1 citation statement)

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“…Now, as one would expect, A-valued inner products naturally give rise to Avalued norms. The existence of the latter has been proved by the present author ( [5]) in the category P(A) of projective finitely generated modules over an appropriate algebra A, thus leading to a generalized Finsler structure on A-bundles (ibid.). Moreover, A-valued norms provide the category P(A) with a differential calculus, which, in turn, allows differential geometric considerations on smooth manifolds and bundles modelled on A-modules ( [6]).…”

Section: Introductionmentioning

confidence: 92%

Translation invariant topologies on commutative *-algebras

Papatriantafillou

1991

Period Math Hung

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Let A be a commutative *-algebra. Under certain conditions on the involution, we construct a topology making A a Hausdorff Q-ring with continuous involution and inversion; this topology is induced by an A-valued norm.Applying the previous considerations to the algebra C(X) of continuous complex-valued functions over a topological space X, we obtain a new characterization of Weierstrass spaces.Furthermore, we provide every projective finitely generated module M over a topological ring R with a unique topology, under which M is a topological R-module and every R-linear map f : M --* N is continuous, for any topological R-module N. In case R = A, we prove that this topology is induced by an A-norm.

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Section: Introductionmentioning

confidence: 92%