If we wish to be aware of the relationship concerning and polynomial rings in a more standard context, it might repay to broaden our scope from polynomial rings to extra standard types of very well-behaved rings.
The rings we’ll be taking into consideration today are classified as the commutative rings of serious-valued steady features with a topological Area with pointwise addition and multiplication. It seems that one can fruitfully interpret ring-theoretic Houses of the ring when it comes to topological Houses of , As well as in particular notably awesome instances one can absolutely recover the Area .
Akhil’s posts at Delta Epsilons in this article and here describe The fundamental Houses of Noetherian rings well, including the proof of the next.
Truly, the creator claims $X$ and $Y$ are hereditarily regionally linked, and this sort of continua are routinely acknowledged being Suslinean.
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At this time I would lean toward the instance remaining right. I actually just have to see that $Y=X/sim$ is Hausdorff.
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