Some research works have mentioned the similarity of autopoiesis with (M,R) systems proposed by Rosen, from the perspective of closedness of the systems. However, there are some difference between the aspects of closedness required for autopoiesis and (M,R) systems. This paper aims at clarifying these differences to investigate the possibility of algebraic description of living systems, based o...

In this paper, we obtain several new generalized KKM-type theorems under a new coercivity condition and the condition of intersectionally closedness which improves condition of transfer closedness. As applications, we obtain new versions of equilibrium problem, minimax inequality, coincidence theorem, fixed point theorem and an existence theorem for an 1-person game.

The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that  the category $L$-$mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.

Defining a system in distinction from its environment is a fundamental but elusive problem in artificial life as well as in real-world complex systems. While many notions of closure gives a qualitative and absolute criteria for the system–environment distinction, the concept of “informational closure” proposed by Bertschinger et al. (Bertschinger et al., 2006, Proc. GWAL-7, p.9, IOS Press) give...

We consider the problem of the semidefinite representation of a class of non-compact basic semialgebraic sets. We introduce the conditions of pointedness and closedness at infinity of a semialgebraic set and show that under these conditions our modified hierarchies of nested theta bodies and Lasserre’s relaxations converge to the closure of the convex hull of S. Moreover, if the PP-BDR property...

In the paper, we describe various applications of the closedness and duality theorems of [7] and [8]. First, the strong separability of a polyhedron and a linear image of a convex set is characterized. Then, it is shown how stability conditions (known from the generalized Fenchel-Rockafellar duality theory) can be reformulated as closedness conditions. Finally, we present a generalized Lagrange...

The projective tensor product in a category of topologicalR-modules (where R is a topological ring) can be defined in Top, the category of topological spaces, by the same universal property used to define the tensor product of R-modules in Set. In this article, we extend this definition to an arbitrary topological category X and study how the cartesian closedness of X is related to the monoidal...

Abrams’ theorem describes a necessary and sufficient condition for the closedness of a linear image of an arbitrary set. Closedness conditions of this type play an important role in the theory of duality in convex programming. In this paper we present generalizations of Abrams’ theorem, as well as Abrams-type theorems characterizing other properties (such as relatively openness or polyhedrality...

Infinite dimensional spaces frequently appear in physics; there are several approaches to obtain a good categorical framework for this type of space, and cartesian closedness of some category, embedding smooth manifolds, is one of the most requested condition. In the first part of the paper, we start from the failures presented by the classical Banach manifolds approach and we will review the m...