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abstract algebra - What's the difference between isomorphism and homeomorphism? - Mathematics Stack Exchange

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Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. I think that they are similar (or same), but I am not sure. Can anyone explain the difference between isomorphism and homeomorphism? Homomorphism - an algebraical term for a function preserving some algebraic operations. For a group homomorphism ϕ 𝜙 we have ϕ(ab)=ϕ(a)ϕ(b) 𝜙 ( 𝑎 𝑏 ) = 𝜙 ( 𝑎 ) 𝜙 ( 𝑏 ) and ϕ(1)=1 𝜙 ( 1 ) = 1 , for a ring homomorphism we have additionally ϕ(a+b)=ϕ(a)+ϕ(b) 𝜙 ( 𝑎 + 𝑏 ) = 𝜙 ( 𝑎 ) + 𝜙 ( 𝑏 ) and for a vector-space homomorphism also ϕ(r⋅a)=r⋅ϕ(a) 𝜙 ( 𝑟 ⋅ 𝑎 ) = 𝑟 ⋅ 𝜙 (

abstract algebra - What's the difference between isomorphism and homeomorphism? - Mathematics Stack Exchange Stack Internal Knowledge at work Bring the best of human thought and AI automation together at your work. Explore Stack Internal What's the difference between isomorphism and homeomorphism? Ask Question Asked 12 years, 7 months ago Modified 9 years, 6 months ago Viewed 37k times 44 $\begingroup$ I think that they are similar (or same), but I am not sure. Can anyone explain the difference between isomorphism and homeomorphism ? abstract-algebra differential-topology Share Cite Follow edi

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