What's the point of topology?

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What's the point of topology?

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>>7843984

T = {S ⊆ X: p ∈ S or S = O}

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>>7843984

the point of topology is to stop posting reddit frogs

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>>7843987

>4chan frogs*

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>>7843986

Where X is any set and p ∈ X

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>>7843986

What's the point of topology in terms of practical usefulness?

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A topology T for a space X gives a rough notion of proximity (eventually relevant for sequences and analysis) and also induces a system of directed arrows on the power set. Continuous functions are an easily definable class of maps special for that topology from or to X and those in turn often translate to morphisms of object on that space. The definitions is actually so rudimentary that it gives rise to dualities all over the place (see Stone duality, Gelfand representation theorems, models for non-classical logics, and stronger notions of topologies (Grothendieck topoi) merge with an even broader class of relevant mathematical objects) It's also a tool to classify sets with other structure (or let's say spaces).

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To make sure graphics in vidya look good

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>autists in this thread are explaining what topology is, rather than what's it for.

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Try doing your silly partial differential equations without topology.

>wuts a limit, lol

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>>7844060

I don't think it answers the question if we refer to topologies induced by metrics

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(or any maps to the reals, tbqh)

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Cant topology be applied to design when you want to design elastic objects?

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Cohomology

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>>7843995

architecture

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>>7843984

Dumb frogposter.

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>>7843995

Topological quantum field theory.

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>>7844053

What's the difference?

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https://en.wikipedia.org/wiki/Topological_data_analysis

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>when am I ever going to need this?

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To impress your friends by writing an equation to theoretically turn a sphere inside out.

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>>7843984

To map the rest of mathematics in a topological space.

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>>7843984

The point is showing that the Earth is indeed flat, because otherwise we'd need to compactify with a single point, and science can't give us any such point

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