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31 Jan 2024: Theorem. There is no group homomorphism F : {0} Z such that the composition. ... such that. f g ' IdY f ′ g′ ' IdZ g f ' IdX g′ f ′ ' IdY.

29 Jan 2024: 4Perhaps the Revelations are not flagged as such? Perhaps checking that something isa revelation involves establishing its independence from earlier revelation? ... Ramsey is such a theorem; Van der Waerdenisn’t! vdW does not prove itself in that way;

29 May 2024: Then there is abijection h: A B. Proof. We seek partitions A = P Q of A and B = R S of B such thatf(P) = R and g(S) = Q. ... then h is a bijection. To see that such partitions exists, let X = P(A) and define H : X X byH(P) = A g(B f(P)).

5 Jun 2024: I)for some small ϵ > 0, but the choice of such is contractible. ... 2.3.1(ii)]. We will write W dp p for such a manifold.

5 Jun 2024: Such a functor F : J Top is said to be continuous if theevaluation map. ... For any closed subset 0 B, let ˜BunMap0 (ξ,π)• denote the semi-simplicialset whose n-simplices consist of bundle maps G : n ξ τn π := (τn B′) (n π) such