the path towards abstraction -- open sets.

🌟Support the channel🌟

🌟my other channels🌟

🌟My Links🌟

🌟How I make Thumbnails🌟

🌟Suggest a problem🌟

[atonaltensor]

I would insert one intermediate step in between open sets in R and topological open sets: the definition of open sets in metric spaces as arbitrary unions of open neighborhoods

[fbkintanar]

This would be a nice place to explain the unexpected asymmetry between the properties for union and intersection. My understanding is that if you allow arbitrary unions of intersections, you might accidentally "capture" or include a limit point which should not be interior. In the case of the Reals, if you have a punctured disk (or the equivalent two intervals on a line) you can consider the intersection of a sequence (of punctured disks) with increasingly smaller diameters. If you allow infinite sequences, you will end up capturing the puncture point, which shouldn't be interior. A more general explanation might have to do with an infinite sequence (or net) capturing the "tail" and generalizing the notion of convergence. If somebody has a better explanation, please share.

[frentz]

Nice video! .. I guess "interior" could use a definition.

[morgengabe]

How come we never use sets as being associative or commutative?
we could express posets as maps from the ordinals to commutative sets, no?

[hypatia-du-bois-marie]

Knock knock who's there? Lawvere, Grothendieck, Lurie.