How Do Topological Closures Relate in Union Operations?

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To prove that the closure of A union B equals the closure of A union the closure of B for non-closed subsets A and B of X, one can utilize definitions and properties of topological closures. Understanding the relationship between set equality and subset inclusion is crucial, as A = B implies A is a subset of B and vice versa. Difficulty in substituting definitions can indicate a deeper issue that may affect future mathematical understanding. Additionally, recommendations for downloading TeX on a new Windows computer include various reliable sources. Mastery of these concepts is essential for progressing in topology and related fields.
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If A and B are two non-closed subsets of X, how would one prove that the closure of A union B= the closure of A union closure of B? Also, what site would you recommend I download TeX from when I get my new computer (Dell, runs on windows)?
 
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A great many problems are trivial if you just restate the problem by substituting in definitions.


And don't forget that, for sets, A = B means the same thing as A \subseteq B \wedge B \subseteq A.



If you have trouble substituting definitions, then this will be a weakness that will cause problems for a long time, so you should work on it specifically. I make a big point of this because it's easy to think that you're just having trouble with the subject material and never remedy the problem... and then it crops up in the next subject, and the next... if it doesn't apply to you, then ignore this paragraph. :smile:
 
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