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 Cx of 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).
