(4.2) Let X = {1,2, 3, 4} and 7 = {0, {1,2,3} , {2, 3},{1},X} be the topology defined on X. (a) Show that the only clopen sets in 7 are X and 0, (b) What can you deduce from the results in (4.2a)?
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- Investigate transfarmation defined as LiR? = B?, L(x,y)=(x+y, x-3) whether the is an isomarphism.2.28 let xa be a translation of R Then (1) La is a continuous bijection from onto R (ii) The image of an open set under Da is an oper set. of (iii) let & be an open set. The component interval +a are exactly The images of the component intervals of the set & under translation a the goal of this section is to establish the following result.Can you have a class boundary that is less than zero? On the probelem I am working, the class goes from 0-5
- 1. (a) (b) (c) (d) Prove or disprove that, for any universal set U and predicates P and Q, [3x = U, P(x) ^ Q(x)] → [3r EU, P(x)) ^ (3x = U, Q(x))] Prove or disprove that, for any universal set U and predicates P and Q, [3r EU, P(x)) ^ (3xU, Q(x))] → [r U, P(x) ^ Q(x)] Prove or disprove that, for any universal set U and predicate P [3r € U, P(x)] → [Vr € U, P(x)] Prove or disprove that, for any universal set U and predicate P [VxU, P(x)] → [3r € U, P(x)]17-#5
- 3 Consider [0, 1] × [0, 1] with dictionary ordering. Find Ã, when A = {(x, y) : 01. Check that the following functions on R² are norms: 1/p a) | (1,72) ||,= (1z1P" + \#a!P), 1sp40 conider the fulloong secempla@rdan oBE. 2 ナメ Assume a solution of the fo rm in I Sux" e) Show that the wecurrence relation Ts Sun + (n+2) + Sw F0, n32 h-2 nt2 (b) shon that the coefficients are (nta) an+ Cnnd (n ti)(hta) C) Show tht a solution of the ODES - s(1-メ+。 +c,(x-$x+ x^_ .., ) 4 40 6) Show that the solution in part a satisfies the origunal oDERecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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