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Since sum which is not necessarily commutative is defined in Omega-algebra A, then Omega-algebra A is called Omega-group. I also considered representation of Omega-group. Norm defined in Omega-group allows us to consider continuity of operations and continuity of representation.
The common in ring, module and algebra is that they are Abelian group with respect to addition. This property is enough to study integration. I treat integral of measurable map into normed Abelian $Omega$-group. Theory of integration of maps into $Om
We prove the Zabreikos lemma in 2-Banach spaces. As an application we shall prove a version of the closed graph theorem and open mapping theorem.
We modify the very well known theory of normed spaces $(E, orm)$ within functional analysis by considering a sequence $( orm_n : ninN)$ of norms, where $ orm_n$ is defined on the product space $E^n$ for each $ninN$. Our theory is analogous to, but
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams which are K
The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed $L^0$-modules (in the sense of Gigli) over a metric measure space.