Algebra

2404 Submissions

[2] viXra:2404.0073 [pdf] submitted on 2024-04-15 15:49:13

On the Classification of the Operational Spaces

Authors: Mathis Antonetti
Comments: 11 Pages.

In this paper, we introduce operational spaces that are a special case of what is usually called quotient topological spaces with an equivalence relation of interest. Then we derive some results and conjectures on their classification and an application to define the convergence of a sequence towards a cycle in the general case. We also provide a perspective on the still unaddressed conjectures concerning the operational spaces and we argue that the commonly useless non-uniform almost periodicity is actually useful in this context to understand the classification of such spaces.
Category: Algebra

[1] viXra:2404.0027 [pdf] submitted on 2024-04-04 00:51:37

Fukaya Categories, Reidemeister Moves, and the Novikov Ring

Authors: Ryan J. Buchanan
Comments: 13 Pages.

We construct a Novikov-type ring and generalize Dirac's $delta$ function into a functor. By applying the generalized $delta$-functor, we are able to reconstruct the Fukaya category $mathscr{B}_0$.
Category: Algebra