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

Maple in Finite Topological Spaces – Special Points

: Taha Guma El Turki
Engineering software solutions from Maplesoft
This Application runs in Maple. Don't have Maple? No problem!
 Try Maple free for 15 days!

Taha Guma Elturki, Kahtan H.Alzubaidy
Department of Mathematics, Faculty of Science, University of Benghazi



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) .


 [1]  Dider Deses  :  Math-Page
 http : //  (2001).

 [2] (2001).

Application Details

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



More Like This

Fractal Dimension and Space-Filling Curves (with iterated function systems)
Rolling without slipping on Mobius strip
Maple in Finite Topological Spaces-Connectedness
Finite Excluded and Included Point Topologies with Maple
Topology with Maple
Topology Package-1
The Extremal and Non-Trivial Minimal Topologies Over a Finite Set with Maple
Cool knots drawn using Maple
MOISE - A Topology Package for Maple
The Extremal and Non-Trivial Minimal Topologies by Definitions