Topology and set theory
Table of Contents
set theories I ve visited
stratified lambda calculus
Think about it
evaluation by reduction ie substituion - integration
confluence is related to convergence
It's somewhat fair to call it calulus, depending on how you see calculus
Bishop's
Russel's
HoTT and Topos
⊥ :≡ 0
T :≡ 1
P ∧ Q :≡ P ∗ Q
P ∨ Q :≡ || P + Q ||
P ⇒ Q :≡ P → Q
∀ (x : A) ⋅ P(x) :≡ ∏ (x:A) ⋅ P(x)
∃ (x : A) ⋅ P(x) :≡ || ∑ (x :A) . P(x) ||
Chesterton
a small circle is quite as infinite as a large circle
cauchy sequences does not have same topology as \R , it has topology of cantor space.
every cauchy real has a dedekind cut
why stop at that
A map f: house -> city between topological spaces is said to be continuous if, for every open set U ∈ (house) , f-1(city) is open in house. 1
Objects of interest
zfc with grothendieck universes - resizing principles, lem, simplical set, fpqc
Question
can sets alone index sets?
Theorems of interest
Banach alaouglu
Banach fixed point
paradoxes
banach tasrki
cantor
Russel
Martin
liar's
Point free Topology
Bye AOC! Hello Constructivism.
| to/as | coq | ||
| reifier | point free | pointed | |
| type declaration | functor | ||
| infix compose | curried function | :: | |
| unix script | sum = foldr (+) 0 | ||
| concatenative land | eval over different categories | ||
Footnotes:
that's right, I just described ε δ definition of limit there.
Created: 2022-11-01 Tue 16:08