In this paper, we propose a novel action-search particle-filtering algorithm for learning processes. This algorithm is designed to perform search domain reduction and heuristic space segmentation. In this method, each action space is divided into new two segments using two particles. Appropriate search domain reduction can minimize learning time and enable the recognition of the evolutionary pr...

In the present paper, we have studied the analogue of some continuous functions in generalized topological space and consequently their behavior in fine topological space (cf. [18]).

Blanck, J., 1997: Computability on topological spaces by eeective domain representations. Our aim in this thesis is to study a uniform method to introduce computability on large, usually uncountable, mathematical structures. The method we choose is domain representations using Scott{Ershov domains. Domain theory is a theory of approximations and incorporates a natural computability theory. This...

For further studying the theory of multigranulation rough sets (MGRS), we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to character...

It is rarely the case that a single electron affects the behaviour of several hundred thousands of atoms. Here we demonstrate a phenomenon where this happens. The key role is played by topological insulators-materials that have surface states protected by time-reversal symmetry. Such states are delocalized over the surface and are immune to its imperfections in contrast to ordinary insulators. ...

A space T is called a linear topological space if (1) T forms a linear f space under operations x+y and ax, where x,yeT and a is a real number, (2) T is a Hausdorff topological space,J (3) the fundamental operations x+y and ax are continuous with respect to the Hausdorff topology. The study § of such spaces was begun by A. Kolmogoroff (cf. [4]. Kolmogoroff's definition of a linear topological s...

We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when ...

We present some sufficient conditions for the existence of a continuous multi-utility representation of a preorder on a topological space (X, τ) (i.e., for the existence of a family F of continuous increasing realvalued functions on the preordered topological space (X, τ, ) such that, for every pair of elements (x, y) ∈ X×X, x y ⇔ f(x) ≤ f(y) ∀f ∈ F). Such conditions are based on the concept of...

Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M . Consider the topological group H(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. We present a complete solution to the topological classification problem for H(M,D) as follows. If M is a o...

The natural duality between “topological” and “regular,” both considered as convergence space properties, extends naturally top-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage of this duality, the behavior ofp-topological andp-regular convergence spaces is explored, with particular emphasis on the former, since they have not been p...