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1
Content available remote On almost e-I-continuous functions
AL-Omeri Wadei, Noiri Takashi
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
168--177
EN
This work is concerned with a new class of functions called almost e-I-continuous functions containing the class of almost e-continuous functions. This notion is stronger than almost δβI-continuous functions and is weaker than both almost e-continuous functions and e-I-continuous functions. Relationships between this new class and other classes of functions are investigated and some characterizations of this new class of functions are studied.
2
Content available remote New soft separation axioms and fixed soft points with respect to total belong and total non-belong relations
Al-shami Tareq M., Tercan Adnan, Mhemdi Abdelwaheb
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
196--211
EN
In this article, we exploit the relations of total belong and total non-belong to introduce new soft separation axioms with respect to ordinary points, namely tt-soft pre Ti (i = 0, 1, 2, 3, 4) and tt-soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft pre-open and pre-closed subsets of soft pre-regular spaces, and second, generalization of existing comparable properties on classical topology. With the help of examples, we show the relationships between them as well as with soft pre Ti (i = 0, 1, 2, 3, 4) and soft pre-regular spaces. Also, we explain the role of soft hyperconnected and extended soft topological spaces in obtaining some interesting results. We characterize a tt-soft pre-regular space and demonstrate that it guarantees the equivalence of tt-soft pre Ti (i = 0, 1, 2). Furthermore, we investigate the behaviors of these soft separation axioms with the concepts of productand sum of soft spaces. Finally, we introduce a concept of pre-fixed soft point and study its main properties.
3
Content available remote Two new forms of ordered soft separation axioms
Al-shami Tareq M., El-Shafei Mohammed E.
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
8--26
EN
The goal of this work is to introduce and study two new types of ordered soft separation axioms, namely soft Ti-ordered and strong soft Ti-ordered spaces (i = 0, 1, 2, 3, 4). These two types are formulated with respect to the ordinary points and the distinction between them is attributed to the nature of the monotone neighborhoods. We provide several examples to elucidate the relationships among these concepts and to show the relationships associate them with their parametric topological ordered spaces and p-soft Ti-ordered spaces. Some open problems on the relationships between strong soft Ti-ordered and soft Ti-ordered spaces (i = 2, 3, 4) are posed. Also, we prove some significant results which associate both types of the introduced ordered axioms with some notions such as finite product soft spaces, soft topological and soft hereditary properties. Furthermore, we describe the shape of increasing (decreasing) soft closed and open subsets of soft regularly ordered spaces; and demonstrate that a condition of strong soft regularly ordered is sufficient for the equivalence between p-soft T1-ordered and strong soft T1-ordered spaces. Finally, we establish a number of findings that associate soft compactness with some ordered soft separation axioms initiated in this work.
4
Content available On e-I-open sets, e-I-continuous functions and decomposition of continuity
Al-Omeri W., Noorani M.S.M., Al-Omari A.
Journal of Mathematics and Applications
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2015
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Vol. 38
15--31
EN
In this paper, we introduce the notations of e-I-open sets and strong B*I -set to obtain a decomposition of continuing via idealization. Additionally, we investigate properties of e-I-open sets and strong B*I -set. Also we studied some more properties of e-I-open sets and obtained several characterizations of e-I-continuous functions and investigate their relationship with other types of functions.
5
Content available remote Open set lattices of subspaces of spectrum spaces
Nai Y. T., Zhao D.
Demonstratio Mathematica
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2015
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Vol. 48, nr 4
637--652
EN
We take a unified approach to study the open set lattices of various subspaces of the spectrum of a multiplicative lattice L. The main aim is to establish the order isomorphism between the open set lattice of the respective subspace and a sub-poset of L. The motivating result is the well known fact that the topology of the spectrum of a commutative ring R with identity is isomorphic to the lattice of all radical ideals of R. The main results are as follows: (i) for a given nonempty set S of prime elements of a multiplicative lattice L, we define the S-semiprime elements and prove that the open set lattice of the subspace S of Spec(L) is isomorphic to the lattice of all S-semiprime elements of L; (ii) if L is a continuous lattice, then the open set lattice of the prime spectrum of L is isomorphic to the lattice of all m-semiprime elements of L; (iii) we define the pure elements, a generalization of the notion of pure ideals in a multiplicative lattice and prove that for certain types of multiplicative lattices, the sub-poset of pure elements of L is isomorphic to the open set lattice of the subspace M ax(L) consisting of all maximal elements of L.
6
Content available remote Some applications of minimal Pγ-open sets
Khalaf A. B., Ibrahim H. Z.
Demonstratio Mathematica
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2014
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Vol. 47, nr 2
423--432
EN
We characterize minimal Pγ-open sets in topological spaces. We show that any nonempty subset of a minimal Pγ-open set is pre Pγ-open. As an application of a theory of minimal Pγ-open sets, we obtain a sufficient condition for a Pγ-locally finite space to be a pre Pγ-Hausdorff space.
7
Content available remote Rδ-supercontinuous functions
Kohli J. K., Tyagi B. K., Singh D., Aggarwal J.
Demonstratio Mathematica
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2014
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Vol. 47, nr 2
433--448
EN
A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl-supercontinuous functions (Demonstratio Math. 46(1) (2013), 229–244) and so includes all cl-supercontinuous (=clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).
8
Content available remote On (γ, γ')-preopen sets
Carpintero C., Rajesh N., Rosas E.
Demonstratio Mathematica
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2013
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Vol. 46, nr 3
617--629
EN
In this paper, we introduce and study the concept of [γ, γ']-preopen sets in topological space.
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