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Topology Construction on The Set of Non-Deranged Permutations Embedded in A Banach Space
Subject area: Science,Engineering and Technology · Area of research: Functional Analysis
DOI: 10.64388/IREV10I2-1712241
Abstract
This work improves on the embedding of groups into Banach space by first reconstructing the group of non deranged permutations into a vector space. We embed the space into a Banach space and define a topology on it. In the Banach space Rn there are many coordinates with different points and some of them are permutations of one or more coordinate points. By embedding a set of non deranged permutations in a Banach space, we seek to understand the set of non deranged permutations in light of the properties of a Banach space. Since Banach space was created to solve problems because a sequence of approximate solutions gets its limit in the Banach space, embedding the set of non deranged permutations in a Banach space makes it possible that a solution to an equation could come out in different permutation patterns. We use isometric embedding method and define a topology on the set. The structure of a topology ensures that the elements of the set can be comparable and relate to one other. The cycles are embedded into each other.
Keywords
non deranged permutations, banach space, topology, embedding
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How to cite this paper
@article{1712241,
author = {Otuekong Udosen Amama, Godwin Ojemeri},
title = {Topology Construction on The Set of Non-Deranged Permutations Embedded in A Banach Space},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {2},
pages = {2758-2763},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1712241.pdf},
abstract = {This work improves on the embedding of groups into Banach space by first reconstructing the group of non deranged permutations into a vector space. We embed the space into a Banach space and define a topology on it. In the Banach space Rn there are many coordinates with different points and some of them are permutations of one or more coordinate points. By embedding a set of non deranged permutations in a Banach space, we seek to understand the set of non deranged permutations in light of the properties of a Banach space. Since Banach space was created to solve problems because a sequence of approximate solutions gets its limit in the Banach space, embedding the set of non deranged permutations in a Banach space makes it possible that a solution to an equation could come out in different permutation patterns. We use isometric embedding method and define a topology on the set. The structure of a topology ensures that the elements of the set can be comparable and relate to one other. The cycles are embedded into each other. },
keywords = {non deranged permutations, banach space, topology, embedding},
month = {August},
doi = {https://doi.org/10.64388/IREV10I2-1712241}
}