Maple in Finite Topological Spaces – Special Points - Maple Application Center
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Maple in Finite Topological Spaces – Special Points

Authors
: Taha Guma el turki
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Taha Guma Elturki, Kahtan H.Alzubaidy
Department of Mathematics, Faculty of Science, University of Benghazi

E-mail: taha1978_2002@yahoo.com, kahtanalzubaidy@yahoo.com

Introduction

The special points of a set in a topological space are limit points, closure points, interior points, boundary points, exterior points, and isolated points. Except limit points and isolated points the other special points can be computed by implementing simple formulas. For limit points we have to resort to the very definition to find them. On the other hand all special points can be derived from limit points. We have found computer procedures to compute the limit points of a set in finite space. Upon these procedures we have created other procedures to find the other special points. The software used is Maple 15. Some ready-made procedures are also used.

Let X be a finite topological space and A is a sub set of X. If the limit points, closure, interior, boundary, exterior and isolated points of A are denoted by LimitPoints(A), ClosurePoints(A), BoundaryPoints(A), InteriorPoints(A), ExteriorPoints(A) and IsolatedPoints(A) respectively, then we have :

ClosurePoints(A) = A U LimitPoints(A) .

BoundaryPoints(A) = ClosurePoints(A) ∩ ClosurePoints(X−A) .

InteriorPoints(A) = ClosurePoints(A) − BoundaryPoints(A) .

ExteriorPoints(A)  = InteriorPoints(X − A) .

IsolatedPoints(A) = A − LimitPoints(A) .

References

 [1]  Dider Deses  :  Math-Page
 http : // student.vub.ac.be./~diddesen/math.html  (2001).

 [2] www.maplesoft.com/applications/view.aspx?SID=4122&view=html (2001).

Application Details

Publish Date: April 07, 2013
Created In: Maple 15
Language: English

Tags

topology

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