Delta neutral: Difference between revisions

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'''Finite topology''' is a mathematical concept which has several different meanings.
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== Finite topological space ==
 
A [[Finite topological space]] is a [[topological space]] whose underlying set is finite.
 
== In endomorphism rings ==
 
If ''A'' and ''B'' are [[abelian groups]] then the '''finite topology''' on the group of homomorphisms Hom(''A'',''B'') can be defined using the following [[Base (topology)|base]] of open neighboourhoods of zero.
 
:<math>U_{x_1,x_2,\ldots,x_n}=\{f\in\operatorname{Hom}(A,B)\mid f(x_i)=0 \mbox{ for } i=1,2,\ldots,n\}</math>
 
This concept finds applications especially in the study of [[endomorphism ring]]s where we have ''A''=''B''. See section 14 of Krylov et al.
<ref>{{citation |last1=Krylov |first1=P.A. |last2=Mikhalev |first2= A.V. |last3=Tuganbaev |first3=A.A. |title=Properties of endomorphism rings of abelian groups I. |journal=J. Math. Sci. (New York)  |volume=112 |year=2002 |pages=4598–4735|mr=1946059}}</ref>
 
== References ==
{{reflist}}
 
[[Category:General topology]]

Latest revision as of 21:31, 11 September 2014

Nice to satisfy you, my name is Refugia. For a while she's been in South Dakota. What I adore doing is playing baseball but I haven't made a dime with it. Bookkeeping is what I do.

My webpage: http://www.dailyroads.com/

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