are bad jokes the whole point of topology? or does it have a point beyond that?
>>16867012Just to entertain your retardation.1. Functional analysis: rigorous notions of local behavior, limits, separation, boundedness, and other notions from analysis that make it possible to generalize to highly abstract spaces like function spaces (Banach, Frechet spaces)2. Metric geometry: topology provides a rigorous way to reason about the above in the context of metric spaces. For example the Hopf-Rinow theorem for geodesic spaces is a vast generalization of the Heine-Borel theorem.3. Order theory: just like metrics induce a unique topology, order relations do so as well. This allows to reason about closedness, limits etc in abstract settings like lattices.4. Measure theory: topology of a space provides a consistent way to construct its measure, eg Borel sets. From this you get “almost everywhere” behavior eg the Rademacher theorem, which is essential for Lebesgue integrability.5. Integration on generic manifolds requires partitions of unity (a concept from topology) to deal with chart transition maps.6. Algebraic topology provides a set of invariants that allow one to compare topological spaces and establish equivalences. This is useful in classifications, such as the simple Lie group classification.7. Cohomology theory is incredibly important in differential geometry and PDE theory as it allows one to generalize the notion of n’th derivatives to a wide class of spaces.There’s like 10000 other things you can mention, but I hope you get the idea.
>>16867021So a bunch of made up bs to hide the hole jokes
>>16867027All math is made up, congrats. You may as well complain about 2+2=4 because you cannot point to the number 2 irl.
>>16867012Isn't there coffee in the donuts on the left?
>>16867012Check the catalog>>16866389
>>16867021Liked & SUBSCRIBED. Thanks, Anon.You the Real MVP.
>>16867012White donut icing, second panel, is very sus.
>>16867058Wait until you bite into one of the right-hand 'donuts' and get a mouthful of scalding hot coffee.Topological humor scars.
>>16867289is this real, chat?
>are bad jokes the whole point of topology?Yes.
>>16867046>all math is made upTell me more about your cult of relative truth and social constructs, while unironically posting it on a system that is the very proof that math is actually beyond just "made up shit that tells illusory stories" but an actual system chain that leads to real world technological expressions of how ridiculous your ignorance-as-an argument is.
>>16867289>>16867313>>16867315Homeomorphisms that are not homo. The topology abides.
>>16867021wheres the funny part?
>>16867012>are bad jokes the whole point of topology? or does it have a point beyond that?If you want an answer to this question, why not consult the introductory pages of friendly textbooks instead of asking in bad faith on a website with awful users. My suggestion:Read the first chapter of Brown's Topology and Grupoids https://groupoids.org.uk/pdffiles/topgrpds-e.pdf as a primer and if you want more at the elementary level, try Olver's Continuous Calculus https://www-users.cse.umn.edu/~olver/ln_/cc.pdf for topology's most basic application and Morris' Topology Without Tears https://www.topologywithouttears.net/topbook.pdf for the most beginner friendly development of the theory
>>16867012It's like category theory (no practical purpose)
>>16868795>It's like category theory (no practical purpose)any good Haskell jokes?
