Topology, Proofs, The word Complement

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Homework Help Overview

The discussion revolves around understanding the term "complement" in the context of a proof related to topology. The original poster is uncertain about the definition and application of this term as it pertains to the complement of a closed interval [a, b].

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster seeks clarification on the meaning of "complement" and expresses a lack of prior knowledge on the topic. Some participants suggest that the complement could refer to the union of intervals outside [a, b], specifically (-∞, a) U (b, ∞). Others provide a resource for further reading to clarify the concept.

Discussion Status

The discussion is ongoing, with participants exploring the definition of "complement" and its implications for the proof. A resource has been shared to aid in understanding the term, but there is no explicit consensus on its meaning yet.

Contextual Notes

The original poster notes the absence of a glossary in their textbook and the lack of prior mention of the term "complement," which adds to their confusion regarding the proof.

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Topology, Proofs, The word "Complement"

Homework Statement


I have a proof to do in which they use the word "complement". I am not sure what it means by that withing the context of the question. There is no glossary to the book and there is no mention of complement before this question.


Homework Equations



Show that the complement of the closed interval [a,b] is an open set.

The Attempt at a Solution



I have not tried it yet because I do not know what they mean by complement. If you could point me to the right website where it talks about this or give a good definition I will then try and finish the proof from there.
 
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The only assumption that I have is that the complement would be (-oo, a) U (b, oo). But still I am not sure if that is what they mean in this context.
 


Thank you so much.
 

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