O Prove that the composition óf önlo
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Q24 a, c
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- 1. Let O1 and O2 be topologies on X. (1) Show that the identity map idX : (X, O1) → (X, O2) is continuous if O2 ⊂ O1. (2) Show that the identity map idX : (X, O1) → (X, O2) is not continuous if O1⊂≠O2.Can you help me explain why T is onto if Rank(T)=2 ?1. Supposef:N→N and g:N→N are functions such that f is not onto but f+g is onto. May we conclude that g is onto? Either give a counter-example or show that g is onto.
- Suppose f : N → N and g : N → N are functions such that f is not onto but f + g is onto. May weconclude that g is onto? Either give a counter-example or show that g is ontoProve that the function f: N --> Z defined by f(n) = [1 + (-1)^n * (2n - 1)] / 4, is bijective.Suppose the function f: X --> Y is onto. Prove or disprove that the induced map f-1: P(Y) --> P(X) is onto. As a first step, make sure to state what it means that a function is onto.