scholarly journals Semi-topological properties

1992 ◽  
Vol 15 (2) ◽  
pp. 267-272
Author(s):  
Bhamini M. P. Nayar ◽  
S. P. Arya
Keyword(s):  
Topological Property ◽  
Topological Properties

A property preserved under a semi-homeomorphism is said to be a semi-topological property. In the present paper we prove the following results: (1) A topological propertyPis semi-topological if and only if the statement(X,𝒯)hasPif and only if(X,F(𝒯))hasP′is true whereF(𝒯)is the finest topology onXhaving the same family of semi-open sets as(X,𝒯), (2) IfPis a topological property being minimalPis semi-topological if and only if for each minimalPspace(X,𝒯),𝒯=F(𝒯).

Separable Topological Space of Hereditary

NUTA Journal ◽  
2020 ◽  
Vol 7 (1-2) ◽  
pp. 68-70
Author(s):  
Raj Narayan Yadav ◽  
Bed Prasad Regmi ◽  
Surendra Raj Pathak
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Sufficient Condition ◽  
Topological Properties ◽  
Necessary And Sufficient Condition ◽  
Separable Space ◽  
Separable Topological Space ◽  
Necessary And Sufficient

A property of a topological space is termed hereditary ifand only if every subspace of a space with the property also has the property. The purpose of this article is to prove that the topological property of separable space is hereditary. In this paper we determine some topological properties which are hereditary and investigate necessary and sufficient condition functions for sub-spaces to possess properties of sub-spaces which are not in general hereditary.

scholarly journals RIEMANNIAN METRIC FOR TEXTURE RECOGNITION

2018 ◽  
pp. 23-27
Author(s):  
Makarenko N.G. ◽  
ChoYong-beom ◽  
Esenaliev A. B.
Keyword(s):  
Riemannian Geometry ◽  
Topological Property ◽  
Riemannian Metric ◽  
Topological Properties ◽  
Connected Component ◽  
Rectangular Coordinate System ◽  
Texture Recognition ◽  
Persistence Diagram ◽  
Cloud Of Points ◽  
Texture Class

The article discusses the recognition of textures on digital images by methods of computational topology and Riemannian geometry. Topological properties of patterns are represented by segments (barcodes) obtained by filtering by the level of photometric measure. Beginning of barcode encodes level at which topological property appears (connected component and/or “hole”), and its end - level at which the property disappears. Barcodes are conveniently parameterized by coordinates of their ends in rectangular coordinate system “birth” and “death” of topological property. Such representation in form of a cloud of points on plane is called a persistence diagram (PD). In the article show that texture class recognition results are significantly better compared to other vectorization methods of PD.

scholarly journals Composable topological properties and semigroups of relations

1970 ◽  
Vol 11 (3) ◽  
pp. 265-275 ◽  
Author(s):  
Kenneth D. Magill
Keyword(s):  
Topological Property ◽  
Topological Spaces ◽  
Topological Properties

It is assumed throughout this paper that all topological spaces under consideration are Hausdorff. Since the notion of topological property is fundamental in this paper, we begin by making it precise. For our purposes here, it is sufficient to think of a topological property Q as being a class of space such that if X ∈ Q and Y is homeomorphic to X, then Y∈Q. To say that a space X has property Q would then be equivalent to saying that X ∈ Q.

scholarly journals Digging for topological property in disordered alloys: the emergence of Weyl semimetal phase and sequential band inversions in PbSe–SnSe alloys

2019 ◽  
Vol 6 (10) ◽  
pp. 2124-2134 ◽  
Author(s):  
Zhi Wang ◽  
Qihang Liu ◽  
Jun-Wei Luo ◽  
Alex Zunger
Keyword(s):  
Topological Property ◽  
Topological Properties ◽  
Weyl Semimetal ◽  
Disordered Alloys

Given that recent search for topological systems has broadened to include alloys where symmetries are broken by substitutional disorder, we try to answer the question of whether topological properties can be preserved, or are modified in such alloys.

Matrix Characterizations of Topological Properties

1968 ◽  
Vol 11 (1) ◽  
pp. 95-105 ◽  
Author(s):  
D.A. Bonnett ◽  
J.R. Porter
Keyword(s):  
Topological Property ◽  
Topological Properties ◽  
Finite Set ◽  
Finite Spaces

In [S], H. Sharp characterizes each topology on a finite set S = {s1, s2,…sn} with a n×n zero-one matrix T = (tij) where tij=1 if and only if . In this paper we seek matrix characterizations of certain topological properties of finite spaces. Such characterizations will provide purely mechanical ways of determining if a space has a certain topological property.

scholarly journals Topological Properties of Four-Layered Neural Networks

2019 ◽  
Vol 9 (2) ◽  
pp. 111-122 ◽  
Author(s):  
M. Javaid ◽  
M. Abbas ◽  
Jia-Bao Liu ◽  
W. C. Teh ◽  
Jinde Cao
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Soft Computing ◽  
Topological Property ◽  
Topological Indices ◽  
Physical Activities ◽  
Topological Properties ◽  
Probabilistic Neural Networks ◽  
Underlying Network

Abstract A topological property or index of a network is a numeric number which characterises the whole structure of the underlying network. It is used to predict the certain changes in the bio, chemical and physical activities of the networks. The 4-layered probabilistic neural networks are more general than the 3-layered probabilistic neural networks. Javaid and Cao [Neural Comput. and Applic., DOI 10.1007/s00521-017-2972-1] and Liu et al. [Journal of Artificial Intelligence and Soft Computing Research, 8(2018), 225-266] studied the certain degree and distance based topological indices (TI’s) of the 3-layered probabilistic neural networks. In this paper, we extend this study to the 4-layered probabilistic neural networks and compute the certain degree-based TI’s. In the end, a comparison between all the computed indices is included and it is also proved that the TI’s of the 4-layered probabilistic neural networks are better being strictly greater than the 3-layered probabilistic neural networks.

scholarly journals Some New Variants of Relative Regularity via Regularly Closed Sets

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Sehar Shakeel Raina ◽  
A. K. Das
Keyword(s):  
Topological Property ◽  
Topological Properties ◽  
Complete Regularity ◽  
Completely Regular ◽  
Closed Sets ◽  
Relative Property ◽  
Relative Version ◽  
The Absolute

Every topological property can be associated with its relative version in such a way that when smaller space coincides with larger space, then this relative property coincides with the absolute one. This notion of relative topological properties was introduced by Arhangel’skii and Ganedi in 1989. Singal and Arya introduced the concepts of almost regular spaces in 1969 and almost completely regular spaces in 1970. In this paper, we have studied various relative versions of almost regularity, complete regularity, and almost complete regularity. We investigated some of their properties and established relationships of these spaces with each other and with the existing relative properties.

Electron Microscopy of Nucleic Acids

1974 ◽  
Vol 32 ◽  
pp. 302-303
Author(s):  
Norman Davidson
Keyword(s):  
Electron Microscopy ◽  
Nucleic Acids ◽  
Basic Protein ◽  
Molecular Biologist ◽  
Topological Properties ◽  
Protein Film ◽  
Polynucleotide Chain

The basic protein film technique for mounting nucleic acids for electron microscopy has proven to be a general and powerful tool for the working molecular biologist in characterizing different nucleic acids. It i s possible to measure molecular lengths of duplex and single-stranded DNAs and RNAs. In particular, it is thus possible to as certain whether or not the nucleic acids extracted from a particular source are or are not homogeneous in length. The topological properties of the polynucleotide chain (linear or circular, relaxed or supercoiled circles, interlocked circles, etc. ) can also be as certained.

The Effect of Topological Properties on Duration Perception of Oddball Stimuli

2013 ◽  
Vol 45 (12) ◽  
pp. 1324-1333
Author(s):  
Baolin LI ◽  
Youguo CHEN ◽  
Xiangyong YUAN ◽  
Jackson Todd ◽  
Xiting HUANG
Keyword(s):  
Topological Properties
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