Supriya Ghosh (Editor)

Finite topology

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

Finite topology is a mathematical concept which has several different meanings.

Contents

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 of open neighbourhoods of zero.

U x 1 , x 2 , … , x n = { f ∈ Hom ⁡ ( A , B ) ∣ f ( x i ) = 0  for  i = 1 , 2 , … , n }

This concept finds applications especially in the study of endomorphism rings where we have A = B. See section 14 of Krylov et al.

References

Finite topology Wikipedia
(Text) CC BY-SA