Recent content by mathshelp

Yea that makes sense. Does anyone know about question iii? Thats the part I'm not sure about really

Regard the n-dimensional real projective space RPn as the space of lines in Rn+1 through {0}, i.e. RPn = (Rn+1 − {0}) /~ with x ~ y if y = λx for λ not equal to 0 ∈ R ;with the equivalence class of x denoted by [x]. (i) Work out the necessary and sufficient condition on a linear map f...

For part ii i was thinking let x be a transitive set which is linearly ordered by ∈. We need to prove that the order is a well-ordering. If not then there is some subset y⊆x which has no ∈ minimal element. Then we have an infinite ∈ chain ∈ an ∈ an-1 ∈... ∈ a1 ∈ y which contradicts the...

Let a and b be sets. Show that the following constructions are sets stating clearly which axioms you need (a) a\b. (b) A function f:a→ b. (c) The image of f. (d) Given that a and b have ranks α and β respectively, what are the maximum possible ranks of a\b, f:a→ b and the...

For part i, is it a contradiction since von neumann ordinals are totally ordered by ∈?

(a) Let α and β be two von Neumann ordinals. Show that α ⊂ β if and only if α ∈ β. (b) Show that the Axiom of Foundation implies that a transitive set which is linearly ordered by ∈ is an ordinal I can't seem to follow through this properly, any help?

That makes sense, but how do you construct a first order formula?

I've come across this question during revision and don't really know what you would say? Any help? Regard a 2 x 2 matrix A as a topological space by considering 2x2 matrices as vectors (a,b,c,d) as a member of R4. Let GL2(R) c R4 be the subset of the 2x2 matrices A which are invertible, i.e...

Write out the proof of Hartog's Theorem again carefully highlighting how the Axiom of Replacement is used How can you highlight the axiom of replacment?

I have a question here and I'm not sure what to do as it always confuses me, any help? Let A,B be closed non-empty subsets of a topological space X with AuB and AnB connected. (i) Prove that A and B are connected. (ii) Construct disjoint non-empty disconnected subspaces A,B c R such...

Homework Statement Let U be a topology on the set Z of integers in which every infinite subset is open. Prove that U is the discrete topology, in which every subset is open. Homework Equations Just the definition of discrete topology The Attempt at a Solution I'm not sure where...

How do you prove the first part of that question?