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Maple in Finite Topological Spaces-Connectedness

Authors
: Taha Guma El Turki
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Maple in Finite Topological Spaces-Connectedness


Taha Guma el turki  , Kahtan H. Alzubaidy

Department of  Mathematics , Faculty of Science ,University of  Benghazi

 e_mails: Taha1978_2002@yahoo.com , Kahtanalzubaidy@yahoo.com

Introduction

Connectedness and path connectedness are equivalent on finite topological spaces [2] .However , one definition of a connected space X is that ∅ and X are the only clopen subsets of X . For x∈ X , the connected component Cof x  is the largest connected subset of  X containing  x .{Cx}x∈X is a partition of  X  and Cx  is clopen for any x∈ X .
We have presented :
i) a new procedure to list all topologies on a finite set .
ii) a procedure to list the connected topologies on a finite set .
iii) a procedure to find the connected components of a finite space .
Maple 15  has been used .

References

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

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

[2]  J.P. May : Finite Topological Spaces
 http://www.math.uchicago.edu/~may/MISC/FiniteSpaces.pdf    (2008).


Application Details

Publish Date: August 20, 2013
Created In: Maple 15
Language: English

Tags

topology

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