scholarly journals Functionally Separation Axioms on General Topology

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Abdelwaheb Mhemdi ◽  
Tareq M. Al-shami
Keyword(s):  
General Topology ◽  
Product Spaces ◽  
Transitive Relation ◽  
New Family ◽  
Separation Axioms ◽  
Hereditary Properties

In this paper, we define a new family of separation axioms in the classical topology called functionally T i spaces for i = 0,1,2 . With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with T i spaces for i = 0,1,2 . We demonstrate that functionally T i spaces are preserved under product spaces, and they are topological and hereditary properties. Moreover, we show that the class of each one of them represents a transitive relation and obtain some interesting results under some conditions such as discrete and Sierpinski spaces.

scholarly journals Two new forms of ordered soft separation axioms

2020 ◽  
Vol 53 (1) ◽  
pp. 8-26
Author(s):  
Tareq M. Al-shami ◽  
Mohammed E. El-Shafei
Keyword(s):  
Finite Product ◽  
Open Problems ◽  
Separation Axioms ◽  
Hereditary Properties

AbstractThe 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.

scholarly journals Partial soft separation axioms and soft compact spaces

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4755-4771 ◽  
Author(s):  
M.E. El-Shafei ◽  
M. Abo-Elhamayel ◽  
T.M. Al-Shami
Keyword(s):  
Topological Space ◽  
General Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Finite Product ◽  
Compact Spaces ◽  
Separation Axioms ◽  
Soft Topological Space

The main aim of the present paper is to define new soft separation axioms which lead us, first, to generalize existing comparable properties via general topology, second, to eliminate restrictions on the shape of soft open sets on soft regular spaces which given in [22], and third, to obtain a relationship between soft Hausdorff and new soft regular spaces similar to those exists via general topology. To this end, we define partial belong and total non belong relations, and investigate many properties related to these two relations. We then introduce new soft separation axioms, namely p-soft Ti-spaces (i = 0,1,2,3,4), depending on a total non belong relation, and study their features in detail. With the help of examples, we illustrate the relationships among these soft separation axioms and point out that p-soft Ti-spaces are stronger than soft Ti-spaces, for i = 0,1,4. Also, we define a p-soft regular space, which is weaker than a soft regular space and verify that a p-soft regular condition is sufficient for the equivalent among p-soft Ti-spaces, for i = 0,1,2. Furthermore, we prove the equivalent among finite p-soft Ti-spaces, for i = 1,2,3 and derive that a finite product of p-soft Ti-spaces is p-soft Ti, for i = 0,1,2,3,4. In the last section, we show the relationships which associate some p-soft Ti-spaces with soft compactness, and in particular, we conclude under what conditions a soft subset of a p-soft T2-space is soft compact and prove that every soft compact p-soft T2-space is soft T3-space. Finally, we illuminate that some findings obtained in general topology are not true concerning soft topological spaces which among of them a finite soft topological space need not be soft compact.

scholarly journals Two Classes of Infrasoft Separation Axioms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Tareq M. Al-shami ◽  
Jia-Bao Liu
Keyword(s):  
Finite Product ◽  
Extensive Discussion ◽  
Fundamental Properties ◽  
Soft Topology ◽  
Separation Axioms ◽  
Hereditary Properties

One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the generalizations of soft topology called infrasoft topology. We first formulate the concepts of infra- t p -soft T j using total belong and partial nonbelong relations and then introduce the concepts of infra- t t -soft T j -spaces using total belong and partial nonbelong relations. To illustrate the relationships between them, we provide some examples. We discuss their fundamental properties and study their behaviors under some special types of infrasoft topologies. An extensive discussion is given for the transmission of these two classes between infrasoft topology and its parametric infratopologies. In the end, we demonstrate which ones have topological and hereditary properties, and we show their behaviors under the finite product of soft spaces.

scholarly journals Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
T. M. Al-shami
Keyword(s):  
Vital Role ◽  
General Topology ◽  
Topological Spaces ◽  
Soft Topology ◽  
Separation Axioms ◽  
The Stability ◽  
Soft Point

The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of t t -soft semi- T i i = 0 , 1 , 2 , 3 , 4 and t t -soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi- T i i = 0 , 1 , 2 , 3 , 4 and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a t t -soft semiregular space and demonstrate that it guarantees the equivalence of t t -soft semi- T i i = 0 , 1 , 2 . Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.

scholarly journals Hereditary properties of semi-separation axioms and their applications

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4689-4700 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Topological Space ◽  
Infinite Product ◽  
Topological Spaces ◽  
Hereditary Property ◽  
Separation Axiom ◽  
Product Property ◽  
Low Level ◽  
Separation Axioms ◽  
Hereditary Properties

The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms such as T1/2 , semi-T1/2 , semi-T1, semi-T2, etc. Besides, using the finite or the infinite product property of the semi-Ti-separation axiom, i ? {1,2}, we prove that the n-dimensional Khalimsky topological space is a semi-T2-space. After showing that not every subspace of the digital topological spaces satisfies the semi-Ti-separation axiom, i ?{1,2}, we prove that the semi-Tiseparation property is open-hereditary, i ? {1,2}. All spaces in the paper are assumed to be nonempty and connected.

Microstructure and crystal symmetry of Pb2Sr2(Y/Ca)Cu3O9−δ

1990 ◽  
Vol 48 (4) ◽  
pp. 64-65
Author(s):  
Y. P. Lin ◽  
J. S. Xue ◽  
J. E. Greedan
Keyword(s):  
Electron Diffraction ◽  
High Temperature Superconductors ◽  
Carbon Film ◽  
Basic Structure ◽  
Crystal Symmetry ◽  
X Ray Diffraction ◽  
X Ray ◽  
Space Groups ◽  
New Family ◽  
Convergent Beam

A new family of high temperature superconductors based on Pb2Sr2YCu3O9−δ has recently been reported. One method of improving Tc has been to replace Y partially with Ca. Although the basic structure of this type of superconductors is known, the detailed structure is still unclear, and various space groups has been proposed. In our work, crystals of Pb2Sr2YCu3O9−δ with dimensions up to 1 × 1 × 0.25.mm and with Tc of 84 K have been grown and their superconducting properties described. The defects and crystal symmetry have been investigated using electron microscopy performed on crushed crystals supported on a holey carbon film.Electron diffraction confirmed x-ray diffraction results which showed that the crystals are primitive orthorhombic with a=0.5383, b=0.5423 and c=1.5765 nm. Convergent Beam Electron Diffraction (CBED) patterns for the and axes are shown in Figs. 1 and 2 respectively.

A new family of fluorescent calcium indicators designed to resist leakage or for measuring calcium near membranes

1994 ◽  
Vol 52 ◽  
pp. 168-169
Author(s):  
Martin Poenie ◽  
Akwasi Minta ◽  
Charles Vorndran
Keyword(s):  
Metal Binding ◽  
Acetoxymethyl Ester ◽  
Binding Properties ◽  
Fura 2 ◽  
New Family ◽  
Anion Transporter ◽  
Calcium Indicator ◽  
Calcium Indicators ◽  
High Calcium ◽  
Intracellular Compartmentalization

The use of fura-2 as an intracellular calcium indicator is complicated by problems of rapid dye leakage and intracellular compartmentalization which is due to a probenecid sensitive anion transporter. In addition there is increasing evidence for localized microdomains of high calcium signals which may not be faithfully reported by fura-2.We have developed a new family of fura-2 analogs aimed at addressing some of these problems. These new indicators are based on a modified bapta which can be readily derivatized to produce fura-2 analogs with a variety of new properties. The modifications do not affect the chromophore and have little impact on the spectral and metal binding properties of the indicator. One of these new derivatives known as FPE3 is a zwitterionic analog of fura-2 that can be loaded into cells as an acetoxymethyl ester and whose retention in cells is much improved. The improved retention of FPE3 is important for both cuvettebased measurements of cell suspensions and for calcium imaging.

Scanning tunneling microscopy and atomic force microscopy: New tools for biology

1989 ◽  
Vol 47 ◽  
pp. 778-779
Author(s):  
CE Bracker ◽  
P. K. Hansma
Keyword(s):  
Physical Property ◽  
Scanning Probe ◽  
Scanning Tunneling ◽  
Small Scale ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
New Family ◽  
Small Probe ◽  
Atomic Force ◽  
Transmission Electron

A new family of scanning probe microscopes has emerged that is opening new horizons for investigating the fine structure of matter. The earliest and best known of these instruments is the scanning tunneling microscope (STM). First published in 1982, the STM earned the 1986 Nobel Prize in Physics for two of its inventors, G. Binnig and H. Rohrer. They shared the prize with E. Ruska for his work that had led to the development of the transmission electron microscope half a century earlier. It seems appropriate that the award embodied this particular blend of the old and the new because it demonstrated to the world a long overdue respect for the enormous contributions electron microscopy has made to the understanding of matter, and at the same time it signalled the dawn of a new age in microscopy. What we are seeing is a revolution in microscopy and a redefinition of the concept of a microscope.Several kinds of scanning probe microscopes now exist, and the number is increasing. What they share in common is a small probe that is scanned over the surface of a specimen and measures a physical property on a very small scale, at or near the surface. Scanning probes can measure temperature, magnetic fields, tunneling currents, voltage, force, and ion currents, among others.

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