In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

Experimental results of the investigation self-healing properties terahertz Bessel beams with orbital angular momentum (OAM) topological charges l=3 and l=4 in free space after passing through a dispersive medium are presented.

Recall that algebraic sets are characterized by resolution tower structures [AK1], [AK2]. A topological space with such a structure is called a T R space for short. In low dimensions existence of resolution tower structures can often be detected by combinatorial invariants of the underlying topological spaces. For example, let X be a locally cone-like Euler stratified space (i.e., a locally con...

Based on the st~uctuzL~m, we propose a generative semantic model which has a topological information space generative grammar as basic rules. In this model a semantic map which is called a topological information space, is generated by the grammar,and the space can express implications and simi l a r i t i e s among concepts. In the syntax, a syntactic generative grammar is defined based on the...

It is the purpose of this paper to prove that if each of X and Y is a compact Hausdorff space containing infinitely many points, and X X Y is the continuous image of a compact ordered space L, then both X and Fare metrizable.2 The preceding theorem is a generalization of a theorem [l ] by Mardesic and Papic, who assume that X, Y, and L are also connected. Young, in [3], shows that the Cartesian...

In [l], we proved a criterion for the disjointness of two induced representations UL and UM of a Lie group G, where L and M are finite-dimensional unitary representations of compact subgroups H and R, respectively, of G. The purpose of this paper is to improve this theorem by getting a stronger conclusion, while dropping the conditions that G be a Lie group and H be compact, and that L and M he...

The smallest and largest elements of L are denoted 0 and 1 respectively, so PL(0) is the empty set and PL(1) is the spectrum of L. As a ranges over L, PL(a) form a basis of closed sets for the so-called Zariski’s topology on Spec(L) which turns Spec(L) into a spectral space, that is a topological space homeomorphic to the spectrum of a ring. The following definitions for an element a and a prim...

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. In consequence, the fundamental group ir(X, Xo) which we obtain frequently reflects local properties which are missed by the usual arcwise group iri(X, Xo). We obtain a perfect Galois theory of covering...

In this paper we study the topological directional entropy of 2  -actions by generated linear cellular automata (CA hereafter), defined by a local rule f[l,r], l, r , l  r, i.e. the maps Tf[l, r]: m m      which are given by Tf[l, r](x) = ( ) n n y   , yn = f(xn+l, ..., xn+r) = r x i n i i l     (mod m), x=    n n x ) (  m   and f: 1 r l m     Zm, over the ring Zm (m...