On minimal λco-open sets

We introduce and discuss the notions of minimal λco-open sets in topological spaces. We establish some of it basic fundamental properties of minimal λco-open. We show that the notions of minimal open sets and minimal λco-open are independent and finally we obtain some application of a minimal λco-open sets

On λ D − R0 And λ D − R1 Spaces

In this paper we introduce the new types of separation axioms called λ D − R0 and λ D − R1 spaces, by using λ D-open set. The notion λ D − R0 and λ D − R1 spaces are introduced and some of their properties are investigated

S-I-convergence of sequences

In this article, we use the notions of a semi-open set and topological ideal, in order to define and study a new variant of the classical concept of convergence of sequences in topological spaces, namely, the S-I-convergence. Some basic properties of S-I-convergent sequences and their preservation under certain types of functions are investigated. Also, we study the notions related to compactness and cluster points by using semi-open sets and ideals. Finally, we explore the Iconvergence of sequences in the cartesian product spac

On decomposition of bioperation-continuity

In this paper, we introduce some new types of sets via bioperation and obtain a new decomposition of bioperation-continuity using this sets

Almost contra (i, j)-continuous multifunctions

The purpose of the present paper is to introduce, study and characterize the upper and lower almost contra (I, J)-continuous multifunctions. Also, we investigate its relation with another well known class of continuous multifunctions

On inversely θ-semi-open and inversely θ-semi-closed functions

In this paper, we introducethe concepts of inversely 6-semi-openandinversely 6-semi-closed functions andobtain their charactcrizationsif it is possible in terms of 6-closure and6-intcrior by using sets determined by thefibres of the function. Finally, we obtainits relationships withthe strongly @-continuous

On real valued ω-continuous functions

The aim of this paper is to introduce and study upper and lower !-continuous functions. Some characterizations and several proper- ties concerning upper (resp. lower) !-continuous functions are obtained

Weakly (I, J)-continuous multifunctions and contra (I, J)-continuous multifunctions

The purpose of the present paper is to introduce, study and characterize upper and lower weakly (I, J)-continuous multifunctions and contra (I, J)-continuous multifunctions. Also, we investigate its relation with another class of continuous multifunctions. AMS Subject Classification: 54C10, 54C08, 54C05, 54C6

Notas sobre propiedades espectrales de un operador, su heredabilidad y aplicaciones

In this paper we describe the behavior of Weyl type theorems or Weyl type properties, for an operator $T$ on a proper closed and $T$-invariant subspace $W\subseteq X$ such that $T^n(X)\subseteq W$, for some $n\geq 1$, where $T\in L(X)$ and $X$ is an infinite-dimensional complex Banach space. Our main purpose is to show that for these subspaces (which generalize the case $T^n(X)$ closed, for some $n\geq 0$) a large number of Weyl type theorems are transmitted from $T$ to its restriction on $W$ and vice-versa. As application of our results, we obtain conditions for which Weyl type theorems are equivalent for two given operators. Also, we give conditions under which an operator acting on a subspace can be extended on the entire space preserving the Weyl type properties.Este art\'{\i}culo versa sobre el comportamiento de los Teoremas, o propiedades, de tipo Weyl para un operador $T$ sobre un subespacio propio cerrado y $T$-invariante $W\subseteq X$ tal que $T^n(X)\subseteq W$, para alg\'{u}n $n\geq 1$, donde $T\in L(X)$ y $X$ es un espacio de Banach complejo e infinito dimensional. Nuestro principal prop\'{o}sito es exhibir que para tales subespacios (los cuales generalizan el caso $T^n(X)$ cerrado, para alg\'{u}n $n\geq 0$), una gran cantidad de Teoremas tipo Weyl se transmiten de $T$ a su restricci\'{o}n sobre $W$ y viceversa. Como aplicaci\'{o}n de nuestros resultados, obtenemos condiciones para que los Teoremas de tipo Weyl sean equivalentes para dos operadores dados. As\'{\i} como tambi\'{e}n, condiciones bajo las cuales un operador que act\'{u}a sobre un subespacio de un espacio dado, pueda extenderse a todo el espacio preserv\'{a}ndose las propiedades tipo Weyl

A note on preservation of spectra for two given operators

We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded p-variation in Wiener’s sense coincide. Additional illustrative results are given too