What do u need to learn topology?

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To learn topology, a foundational understanding of basic set theory and algebra is essential. Familiarity with analysis can significantly enhance comprehension of topological concepts. A topology on a set X consists of subsets that meet specific axioms, such as including X and the empty set, and allowing for arbitrary unions and finite intersections. Examples of topologies include the trivial topology and the cofinite topology. Overall, while additional knowledge may be beneficial, a solid grasp of set theory and algebra is sufficient to begin studying topology.
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wat do u need to learn topology?
 
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Familiarity with analysis, and some algebra would help too...
 
what do you need to learn anything?

in this case you need to be not scared when I say the following:

If X is a set, then a topology on X is a collection of subsets T in P(X) (the power set) satisfying the following axioms:

X is in T, the empty set is in T, the union of arbitrarily many elements of T is an element of T, and the finite intersection of elements of T is an element of T.

That is exactly what a topology of open sets on X is. Examples: the trivial topology: T is the empty set and X alone

The cofinite topology, T contains the empty set, X and precisely those subsets of X whose complements are finite.

If X is a metric space then the open sets in the metric are a topology.

If any or all of that is too daunting then learn some more set theory and analysis
 
Last edited:
michealsmith said:
wat do u need to learn topology?

Basic set theory and algebra -- that's about it. Depending on how the course is taught, other stuff will definitely be handy, but not actually essential. That said, a lot of topology will make more sense if you have exposure to concepts from analysis.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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