scholarly journals Soft Ideal Theory Soft Local Function and Generated Soft Topological Spaces

2014 ◽  
Vol 8 (4) ◽  
pp. 1595-1603 ◽  
Author(s):  
A. Kandil ◽  
O. A. E. Tantawy ◽  
S. A. El-Sheikh ◽  
A. M. Abd El-latif
Keyword(s):  
Ideal Theory ◽  
Topological Spaces ◽  
Local Function

scholarly journals Local function versus local closure function in ideal topological spaces

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3725-3731 ◽  
Author(s):  
Aleksandar Pavlovic
Keyword(s):  
Function Versus ◽  
Topological Spaces ◽  
Local Function ◽  
Local Closure ◽  
Closure Function ◽  
Similarities And Differences

The aim of this paper is to further investigate properties of the local closure function, as a generalization of the ?-closure and the local function in ideal topological spaces. Similarities and differences between it and the local function are examined by varying several well-known ideals.

Pre-Local Function in Ideal Topological Spaces

2021 ◽  
Vol 8 (1) ◽  
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function

The aim of this paper is to introduce the notation of pre-local function A^(p^* )(I, ?) by using pre-open sets in an ideal topological space (X, ?, I). Some properties and characterizations of a pre-local function are explored Pre-compatible spaces are also defined and investigated. Moreover, by using A^(p^* )(I, ?) we introduce an operator ?: P(X)?? satisfying ?(A) = X-?(X-A)?^(p^* )for each A ? P(X) and we discuss some characterizations this operator by use pre-open sets.

scholarly journals The prime and maximal spectra and the reticulation of residuated lattices with applications to De Morgan residuated lattices

2020 ◽  
Vol 18 (1) ◽  
pp. 1206-1226
Author(s):  
Liviu-Constantin Holdon
Keyword(s):  
Residuated Lattice ◽  
Ideal Theory ◽  
Residuated Lattices ◽  
Proper Ideal ◽  
Distributive Lattices ◽  
Topological Spaces ◽  
Zariski Topology ◽  
Lattice Of Ideals ◽  
The Ideal

Abstract In this paper, by using the ideal theory in residuated lattices, we construct the prime and maximal spectra (Zariski topology), proving that the prime and maximal spectra are compact topological spaces, and in the case of De Morgan residuated lattices they become compact {T}_{0} topological spaces. At the same time, we define and study the reticulation functor between De Morgan residuated lattices and bounded distributive lattices. Moreover, we study the I-topology (I comes from ideal) and the stable topology and we define the concept of pure ideal. We conclude that the I-topology is in fact the restriction of Zariski topology to the lattice of ideals, but we use it for simplicity. Finally, based on pure ideals, we define the normal De Morgan residuated lattice (L is normal iff every proper ideal of L is a pure ideal) and we offer some characterizations.

scholarly journals Generalized open sets in grill N-topology

2017 ◽  
Vol 18 (2) ◽  
pp. 289
Author(s):  
M. Lellis Thivagar ◽  
Ivan L Reilly ◽  
M. Arockia Dasan ◽  
V. Ramesh
Keyword(s):  
Topological Spaces ◽  
Local Function ◽  
Systematic Development

The aim of this paper is to give a systematic development of grill N-topological spaces and discuss a few properties of local function. We build a topology for the corresponding grill by using the local function. Furthermore, we investigate the properties of weak forms of open sets in the grill N-topological spaces and discuss the relationships between them.

scholarly journals Study on Feebly Local Function

2018 ◽  
Vol 7 (3.27) ◽  
pp. 516
Author(s):  
Afeefa Yousif Jaafar Al-Fahham ◽  
Yiezi Kadham Altalkany
Keyword(s):  
Topological Spaces ◽  
Local Function ◽  
New Type

A new type of local function in ideal topological spaces was submitted with some theorems and relations between the new type of local function and other types 

scholarly journals Soft Semi Local Functions in Soft Ideal Topological Spaces

2019 ◽  
Vol 12 (3) ◽  
pp. 857-869
Author(s):  
Fatouh Gharib ◽  
Alaa Mohamed Abd El-latif
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function ◽  
Soft Sets ◽  
Soft Topology ◽  
Local Functions ◽  
Equivalent Conditions

In this paper, we define a soft semi local function (F, E) ∗s ( ˜I, τ ) by using semi open soft sets in a soft ideal topological space (X, τ, E, ˜I). This concept is discussed with a view to find new soft topologies from the original one, called ∗s-soft topology. Some properties and characterizations of soft semi local function are explored. Finally, the notion of soft semi compatibility of soft ideals with soft topologies is introduced and some equivalent conditions concerning this topic are established here.

scholarly journals Fuzzy Ideal Supra Topological Spaces

2020 ◽  
Author(s):  
Fadhil Abbas
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Basic Structure ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Local Function ◽  
Closed Sets ◽  
Fuzzy Ideal ◽  
Neighbourhood Structure

Abstract In this paper, we introduce the notion of fuzzy ideals in fuzzy supra topological spaces. The concept of a fuzzy s-local function is also introduced here by utilizing the s-neighbourhood structure for a fuzzy supra topological space. These concepts are discussed with a view to nd new fuzzy supra topologies from the original one. The basic structure, especially a basis for such generated fuzzy supra topologies and several relations between different fuzzy ideals and fuzzy supra topologies are also studied here. Moreover, we introduce a fuzzy set operator ΨS and study its properties. Finally, we introduce some sets of fuzzy ideal supra topological spaces (fuzzy *-supra dense-in-itself sets, fuzzy S*-supra closed sets, fuzzy *-supra perfect sets, fuzzy regular-I-supra closed sets, fuzzy-I-supra open sets, fuzzy semi-I-supra open sets, fuzzy pre-I-supra open sets, fuzzy α-I-supra open sets, fuzzy β-I-supra open sets) and study some characteristics of theses sets and then we introduce some fuzzy ideal supra continuous functions.

scholarly journals Rings which resemble rings of entire functions

1983 ◽  
Vol 24 (1) ◽  
pp. 7-16
Author(s):  
David E. Rush
Keyword(s):  
Riemann Surface ◽  
Partially Ordered Set ◽  
Riemann Surfaces ◽  
Entire Functions ◽  
Ordered Set ◽  
Ideal Theory ◽  
Prime Ideals ◽  
Topological Spaces ◽  
Valuation Theory ◽  
The Ideal

Since Helmer's 1940 paper [9] laid the foundations for the study of the ideal theory of the ring A(ℂ) of entire functions, many interesting results have been obtained for the rings A(X) of analytic functions on non-compact connected Riemann surfaces. For example, the partially ordered set Spec (A(ℂ) of prime ideals of A(ℂ) has been described by Henrikson and others [2], [10], [11]. Also, it has been shown by Ailing [4] that Spec(A(ℂ))sSpec(A(X)) as topological spaces for any non-compact connected Riemann surface X. Many results on the valuation theory of A(X) have also been obtained [1], [2]. In this note we show that a large portion of the results on the rings A(X) extend to the W-rings with complete principal divisor space which were defined by J. Klingen in [15], [16]. Therefore, many properties of A(ℂ) are shared by its non-archimedian counterparts studied by M. Lazard, M. Krasner, and others [8], [17], [18].

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