[13] **viXra:1310.0219 [pdf]**
*submitted on 2013-10-24 17:06:41*

**Authors:** A. A. Salama, Mohamed Eisa, Florentin Smarandache

**Comments:** 2 Pages. In this paper we generalize the classical topological spaces to the notion of neutrosophic classical set. Finally, we construct the basic concepts of the neutrosophic classical topology and we obtain several properties. Possible application to GIS topolog

In this paper we generalize the classical topological spaces to the notion of neutrosophic classical set. Finally, we construct the basic concepts of the neutrosophic classical topology and we obtain several properties. Possible application to GIS topology rules are touched upon.

**Category:** Topology

[12] **viXra:1310.0218 [pdf]**
*submitted on 2013-10-24 17:08:56*

**Authors:** A. A. Salama, Mohamed Eisa, Florentin Smarandache

**Comments:** 2 Pages. In this paper we introduce the notion of filters on neutrosophic classical set which is considered as a generalization of filters studies, the important neutrosophic classical filters has been given. Several relations between different neutrosophic classi

In this paper we introduce the notion of filters on neutrosophic classical set which is considered as a generalization of filters studies, the important neutrosophic classical filters has been given. Several relations between different neutrosophic classical filters and neutrosophic topologies are also studied here. Possible applications to database systems are touched upon.

**Category:** Topology

[11] **viXra:1310.0216 [pdf]**
*submitted on 2013-10-24 17:16:23*

**Authors:** A. A. Salama, Mohamed Eisa, Florentin Smarandache

**Comments:** 2 Pages.

In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important topological neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to find new neutrosophic topology from the original one in [8]. The basic structure, especially a basis for such generated neutrosophic topologies and several relations between different topological neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules are touched upon.

**Category:** Topology

[10] **viXra:1310.0198 [pdf]**
*submitted on 2013-10-23 00:00:41*

**Authors:** Nathan O. Schmidt

**Comments:** 9 pages, accepted in the Hadronic Journal

In this exploration, we introduce and define "dynamic iso-spaces", which are cutting-edge iso-mathematical constructions that are built with "dynamic iso-topic liftings" for "dynamic iso-unit functions". For this, we consider both the continuous and discrete cases. Subsequently, we engineer two simple examples that engage Fibonacci's sequence and Mandelbrot's set to define a "Fibonacci dynamic iso-space" and a "Mandelbrot dynamic iso-space", respectively. In total, this array of resulting iso-structures indicates that a new branch of iso-mathematics may be in order.

**Category:** Topology

[9] **viXra:1310.0096 [pdf]**
*submitted on 2013-10-13 17:21:15*

**Authors:** A.A. Salama, S.A. Alblowi

**Comments:** 5 Pages. Neutrosophy has been introduced by Smarandache [7, 8] as a new branch of philosophy. The purpose of this paper is to construct a new set theory called the neutrosophic set. After given the fundamental definitions of neutrosophic set operations, we obtain

Neutrosophy has been introduced by Smarandache [7, 8] as a new branch of philosophy. The
purpose of this paper is to construct a new set theory called the neutrosophic set. After given the fundamental
definitions of neutrosophic set operations, we obtain several properties, and discussed the relationship between
neutrosophic sets and others. Finally, we extend the concepts of fuzzy topological space [4], and intuitionistic
fuzzy topological space [5, 6] to the case of neutrosophic sets. Possible application to superstrings and
space–time are touched upon.

**Category:** Topology

[8] **viXra:1310.0092 [pdf]**
*submitted on 2013-10-13 07:16:37*

**Authors:** A.A.Salama

**Comments:** 7 Pages. Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have be

Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have been introduced to fuzzy topological spaces in the last twenty years but not have been studied using fuzzy ideals so,the main aim of our work in this paper is to define and study some new various types of fuzzy compactness with respect to fuzzy ideals namely fuzzy L-compact and L*-compact spaces. Also fuzzy compactness with respect to ideal is useful as unification and generalization of several others widely studied concepts. Possible application to superstrings and E∞ space-time are touched upon.

**Category:** Topology

[7] **viXra:1310.0089 [pdf]**
*submitted on 2013-10-13 07:29:00*

**Authors:** M. E. Abd El-Monsef, A.Kozae, A. A. Salama, H.M.Elagmy

**Comments:** 5 Pages. In this paper we introduce the notion of fuzzy bitopological ideals .The concept of fuzzy pairwise local function is also introduced here by utilizing the q-neighborhood structure for a fuzzy topological space .These concepts are discussed fuzzy bitopolog

In this paper we introduce the notion of fuzzy bitopological ideals .The concept of fuzzy pairwise
local function is also introduced here by utilizing the q-neighborhood structure for a fuzzy topological space
.These concepts are discussed fuzzy bitopologies and several relations between different fuzzy bitopological
ideals .

**Category:** Topology

[6] **viXra:1310.0087 [pdf]**
*submitted on 2013-10-13 07:38:01*

**Authors:** A.A.Salama

**Comments:** 4 Pages. In this paper, fuzzy L-open sets due to Abd El-Monsef et al. [4] are used to introduce a new separation axiom and new type of function in fuzzy topological ideals spaces . Some the basic properties of fuzzy L-irresolute functions, as well as the connectio

In this paper, fuzzy L-open sets due to Abd El-Monsef et al. [4] are used to introduce a new
separation axiom and new type of function in fuzzy topological ideals spaces . Some the basic properties of fuzzy
L-irresolute functions, as well as the connections between them, are investigated. Possible application to
superstrings and space–time are touched upon.

**Category:** Topology

[5] **viXra:1310.0086 [pdf]**
*submitted on 2013-10-13 07:40:55*

**Authors:** M. E. Abd El-Monsef, A. Kozae, A. A. Salama, H. M. Elagamy

**Comments:** 4 Pages. The aim of this paper is to introduce and study some new fuzzy pairwise notion in fuzzy bitopological ideals spaces. We also generalize the notion of fuzzy L-open sets due to Abd El-Monsef et al[1]. In addit ion to generalize the concept of fuzzy L-closed

The aim of this paper is to introduce and study some new fuzzy pairwise notion in fuzzy bitopological ideals
spaces. We also generalize the notion of fuzzy L-open sets due to Abd El-Monsef et al[1]. In addit ion to generalize the
concept of fuzzy L-closed sets, fuzzy L-continuity and L-open functions due to Abd El-Monsef et al[1]. Relationships
between the above new fuzzy pairwise notions and there other relevant classes are investigated. Recently, we define and
study two different types of fuzzy pairwise functions .

**Category:** Topology

[4] **viXra:1310.0085 [pdf]**
*submitted on 2013-10-13 07:43:52*

**Authors:** A. A. Salama, S. A. Alblowi

**Comments:** 5 Pages. In this paper we introduce the notion of generalized intuitionistic fuzzy ideals which is considered as a generalization of fuzzy intuitionistic ideals studies in[6], the important generalized intuitionistic fuzzy ideals has been given. The concept of gen

In this paper we introduce the notion of generalized intuitionistic fuzzy ideals which is considered as a generalization of fuzzy intuitionistic ideals studies in[6], the important generalized intuitionistic fuzzy ideals has been given. The concept of generalized intuitionistic fuzzy local function is also introduced for a generalized intuitionistic fuzzy topological space. These concepts are discussed with a view to find new generalized intuitionistic fuzzy topology from the original one in[5, 7]. The basic structure, especially a basis for such generated generalized intuitionistic fuzzy topologies and several relations between different generalized intuitionistic fuzzy ideals and generalized intuitionistic fuzzy topologies are also studied here.

**Category:** Topology

[3] **viXra:1310.0084 [pdf]**
*submitted on 2013-10-13 07:48:25*

**Authors:** A.A. Salama, S.A. Alblowi

**Comments:** 10 Pages. In this paper we introduce the notion of intuitionistic fuzzy ideals which is considered as a generalization of fuzzy ideals studies in [1, 2, 3, 11 ], the important intuitionistic fuzzy ideal has been given. The concept of intuitionistic fuzzy local func

In this paper we introduce the notion of intuitionistic fuzzy ideals which is
considered as a generalization of fuzzy ideals studies in [1, 2, 3, 11 ], the
important intuitionistic fuzzy ideal has been given. The concept of
intuitionistic fuzzy local function is also introduced here by utilizing the -
neighborhood structure for an intuitionistic fuzzy topological space. These
concepts are discussed with a view to find new intuitionistic fuzzy topology
from the original one in [10, 12].The basic structure, especially a basis for
such generated intuitionistic fuzzy topologies and several relations between
different intuitionistic fuzzy ideals and intuitionistic fuzzy topologies are also
studied here. Finally, several properties of all investigated new notions are
discussed.

**Category:** Topology

[2] **viXra:1310.0083 [pdf]**
*submitted on 2013-10-13 07:50:40*

**Authors:** M.e. Abd El-Monsef, A.a. Nasef, A.a. Salama

**Comments:** 11 Pages. Recently in 1997, Sarker in [8] introduced the concept of fuzzy ideal and fuzzy local function between fuzzy topological spaces. In the present paper, we introduce some new fuzzy notions via fuzzy ideals. Also, we generalize the notion of L-open sets due

Recently in 1997, Sarker in [8] introduced the concept of
fuzzy ideal and fuzzy local function between fuzzy topological spaces.
In the present paper, we introduce some new fuzzy notions via fuzzy
ideals. Also, we generalize the notion of L-open sets due to Jankovic
and Homlett [6]. In addition to, we generalize the concept of L-closed
sets, L- continuity due to Abd El-Monsef et al. [2]. Relationships
between the above new fuzzy notions and other relevant classes are
investigated.1

**Category:** Topology

[1] **viXra:1310.0079 [pdf]**
*submitted on 2013-10-12 19:35:26*

**Authors:** A. A. Salama, S. A. Alblowi

**Comments:** 4 Pages.

In this paper we introduce definitions of generalized neutrosophic sets. After given the fundamental definitions
of generalized neutrosophic set operations, we obtain several properties, and discussed the relationship between generalized
neutrosophic sets and others. Finally, we extend the concepts of neutrosophic topological space [9], intuitionistic fuzzy
topological space [5, 6], and fuzzy topological space [4] to the case of generalized neutrosophic sets. Possible application to
GIS topology rules are touched upon.

**Category:** Topology