An application of relative topology in biology

2009 ◽  
Vol 42 (1) ◽  
pp. 202-204
Author(s):  
S.I. Nada ◽  
H. Zohny
Keyword(s):  
Relative Topology

scholarly journals Transitive maps in bitopological dynamical systems

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2011-2021
Author(s):  
Santanu Acharjee ◽  
Kabindra Goswami ◽  
Hemanta Sarmah
Keyword(s):  
Dynamical Systems ◽  
Human Embryo ◽  
Development Process ◽  
Biological Application ◽  
Relative Topology

This paper introduces fundamental ideas of bitopological dynamical systems. Here, notions of bitopological transitivity, point transitivity, pairwise iterated compactness, weakly bitopological transitivity, etc. are introduced. Later, it is shown that under pairwise homeomorphism, weakly point transitivity implies weakly bitopological transitivity. Moreover, under pairwise homeomorphism; pairwise compactness and pairwise iterated compactness are found to be equivalent. Later, we apply our results in the development process of a human embryo from the zygote until birth. During the process of biological application, we disprove conjecture 1 of Nada and Zohny [S. I. Nada, H. Zohny, An application of relative topology in biology. Chaos, Solitons and Fractals, 42 (2009) 202-204].

On quasi-irresolute characterization of topological loops

2021 ◽  
Vol 104 (4) ◽  
pp. 003685042110445
Author(s):  
Hanan Alolaiyan ◽  
Kashif Maqbool ◽  
Awais Yousaf ◽  
Abdul Razaq
Keyword(s):  
Relative Topology ◽  
Inverse Property

In this paper, we investigate and explore the properties of quasi-topological loops with respect to irresoluteness. Moreover, we construct an example of a quasi-irresolute topological inverse property-loop by using a zero-dimensional additive metrizable perfect topological inverse property-loop [Formula: see text] with relative topology [Formula: see text].

The Bott Suspension and the Intrinsic Join

1975 ◽  
Vol 27 (6) ◽  
pp. 1211-1221
Author(s):  
James A. Leise
Keyword(s):  
Topological Group ◽  
Relative Topology ◽  
Image Position

If (G ; U, V) is a triad with G a group we definewhere [g, u] = gug-1u-1 is the commutator. CG(U, V) will be called the (left) center of U in G modulo V or in brief a (left) C-space. If G is a topological group it will be understood that the topology on CG(U, V) is the relative topology of G.

scholarly journals New Soft Structure: Infra Soft Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Closure Operators ◽  
Relative Topology ◽  
Closed Sets ◽  
Soft Topology ◽  
Soft Limit ◽  
Basic Concepts ◽  
Soft Topological Space

It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

scholarly journals A Topology on a Hyper BCI-algebra Generated by a Hyper-order

2021 ◽  
Vol 14 (2) ◽  
pp. 590-600
Author(s):  
Michelle Panganduyon ◽  
Sergio Rosales Canoy Jr. ◽  
Bijan Davvaz
Keyword(s):  
Relative Topology ◽  
The Family ◽  
Hyper Order ◽  
Induced Topology

In this paper, we introduce an operator on a hyper BCI-algebra via application of aleft hyper-order. The family consisting of the images of subsets under the operator turns out to be a base for some topology on the hyper BCI-algebra. We investigate some important properties of the induced topology on certain hyper BCI-algebras. In particular, we show that the generated topology on a non-trivial hyper subalgebra of an ordered hyper BCI-algebra coincides with the relative topology on this hyper subalgebra.

scholarly journals On Measure of Sum Sets III

1964 ◽  
Vol 14 (2) ◽  
pp. 165-166
Author(s):  
A. M. Macbeath
Keyword(s):  
Relative Topology ◽  
Closed Sets

In my paper on the continuous (α + β) – theorem (these Proceedings 12 (1961), 209–211) the proof of Lemma 6 assumes that if A and B are closed sets in the relative topology as subsets of the space P of positive reals then C = A + B is closed.

scholarly journals On forward iterated Hausdorffness and development of embryo from zygote in bitopological dynamical systems

2021 ◽  
Vol 13(62) (2) ◽  
pp. 399-410
Author(s):  
Santanu Acharjee ◽  
Kabindra Goswami ◽  
Hemanta Kumar Sarmah
Keyword(s):  
Dynamical System ◽  
Cell Division ◽  
Dynamical Systems ◽  
Topological Space ◽  
Development Process ◽  
Hausdorff Space ◽  
Topological Dynamical System ◽  
Relative Topology ◽  
Dynamical Properties

Topological dynamical system is an area of dynamical system to investigate dynamical properties in terms of a topological space. Nada and Zohny [Nada, S.I. and Zohny, H., An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202-204] applied topological dynamical system to explore the development process of an embryo from the zygote until birth and made three conjectures. In this paper, we disprove conjecture 3 of Nada and Zohny [Nada, S.I. and Zohny, H., An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202-204] by applying some of our mathematical results of bitopological dynamical system. Also, we introduce forward iterated Hausdorff space, backward iterated Hausdorff space, pairwise iterated Hausdor_ space and establish relations between them in bitopological dynamical system. We formulate the function that represents cell division (specially, mitosis) and using this function we show that in the development process of a human baby from the zygote until its birth, there is a stage where the developing stage is forward iterated Hausdorff

Extension of Coverings, of Pseudometrics, and of Linear-Space-Valued Mappings

1953 ◽  
Vol 5 ◽  
pp. 211-215 ◽  
Author(s):  
Richard Arens
Keyword(s):  
Topological Space ◽  
Linear Space ◽  
Closed Subset ◽  
Open Covering ◽  
Relative Topology

Let A be a closed subset of a topological space. We show that the following three conditions are equivalent.1.1 Any countable neighbourhood-finite open covering of A (the topological terms referring to the relative topology of A) has a refinement which can be extended to be a countable neighbourhood-finite open covering of X.

scholarly journals Finite products of limits of direct systems induced by maps

2015 ◽  
Vol 16 (2) ◽  
pp. 209 ◽  
Author(s):  
Ivan Ivansic ◽  
Leonard R. Rubin
Keyword(s):  
Direct Limit ◽  
Finite Product ◽  
Relative Topology ◽  
Finite Products

Let Z, H be spaces. In previous work, we introduced the<br />direct (inclusion) system induced by the set of maps between the spaces Z and H. Its direct limit is a subset of Z × H, but its topology is different from the relative topology. We found that many of the spaces constructed from this method are pseudo-compact and Tychonoff. We are going to show herein that these spaces are typically not sequentially compact and we will explore conditions under which a finite product of them will be pseudo-compact.

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