Limits of functions and sequences

In summary, the conversation discusses the concept of functions and limits in different mathematical spaces, including euclidean spaces and topological spaces. The topic of continuity and differentiation is brought up, as well as the possibility of a function having limits at points. The existence and uniqueness of limits in different types of spaces, such as metric spaces and Hausdorff spaces, is also discussed. The conversation ends with a mention of the Zariski topology and its implications on the concept of limits in algebraic geometry.
  • #36
excellent point! you are quite right that one should consider also possibly reducible curves, but i tend to think of irreducible ones. So, good point well taken, a closed subset of a reducible curve may not be finite, it might be a whole component! so maybe add "irreducible" to my statements about curves.
 
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  • #37
mathwonk said:
but i tend to think of irreducible ones.
I think this makes a lot of sense, given your background.

Thank you, and also @WWGD, for the little discussion.
 

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