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Topology
Open sets, continuity, compactness, connectedness: geometry without distance.
Mësime
distance between (1,2) and (4,6)
Core
Compactness and connectedness
The two properties that make theorems work: extreme values and intermediate values.
critical points of x^3 - 3x
Advanced
Homeomorphism and topological invariants
When two spaces are "the same", and what numbers survive stretching.
12 - 30 + 20
What survives when you are allowed to stretch but not tear. Topology makes "nearby" precise without a ruler, and its invariants (connected pieces, holes) are the coarsest and most robust things a space has.
Mësime
Spaces
Continuity and separation
Compactness and connectedness
Where it leads
Disa nga këto mësime janë përshtatur nga tekstet e hapura: Wikipedia. Çdo faqe mësimi emëron burimin dhe licencën e saj.
Simbolet e përdorura këtu
Prek çdo simbol për përkufizimin e plotë, një fotografi dhe se çfarë do të thotë çdo shkronjë në të.
Pyetja që bëjnë njerëzit
Why "a doughnut is a coffee cup"?
Each can be deformed into the other without cutting or gluing: one hole each. Topology studies exactly the properties such deformations preserve.
What is compactness for?
It is the property that makes "every sequence has a convergent subsequence" and "continuous functions attain their maximum" true. On the real line it means closed and bounded.
Shkruaj ose vizato në faqen e zgjidhjes: çdo hap, një fotografi, përgjigja e fshehur deri sa të pyesësh. Zgjidh →
Degë të tjera
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