2) Let n E N. Suppose An = {n, n+ 1, n +2, ...} and T ={0, An}neN•(a) Show that t is a topology on N,(b) What are closed sets in t?(c) List the open sets containing the positive integer 6.(d) What is the closure of {4} and {2,4,6, 8, . ..}?

As per the guideline, we are supposed to do the first three subparts of a problem. Kindly repost the…

Answered: Let n e N. Suppose An = {n,n +1, n…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Solve for B please.
-, answer the following questions: -w³ (w+2) ³ (w - 4) ³ (w - 3) Given m(w) w7 (w + 2) (w-3)³ (w +9)¹ Round all answers to 3 decimal places as needed. If the answer doesn't exist, type DNE. a) The domain of m in set notation and interval notation is: Set Notation: {w w is a real number and w Interval Notation: 0 (-∞, -9) U (-9, -2) U (-2, 0) U (0, 3) U (3, ∞0) b) The w-intercept(s) are: c) The vertical asymptotes of m are at w Write the answer(s) as just numbers separated by commas. d) m has a hole at the ordered pair: Write each hole as an ordered pair. Do not do any rounding until the final answer. e) The m(w)-intercept is: ODNE f) The end behavior of m is: RH: As w LH: As or wor → m(w) Om(w) -∞ (4,0) 8 -9,-2,0,3 Horizontal Asymptote: DNE Write the horizontal asymptote as y = # if it exists. If it doesn't exist, type DNE. OF 0, 9 (3,0), (-2, 607.247)
Q1 Let N be the set of all positive integers. Prove that each of the following collections of subsets of N is a topology. (i) Tị consists of N, Ø, and every set {1,2, ..., n}, for n any positive integer. (This is called the initial segment topology.) (ii) T2 consists of N, Ø, and every set {n, n+1,. }, for n any positive integer. ... (This is called the final segment topology.)
Consider the family of sets S= [{1,5, 6}, {2,4, 6), (4, 5, 6), {2, 5, 6}, {3,4, 5}, {1, 4, 6}]. (1.1) and let Y - (1,3, 4, 5}. Define the relation Ron S by (A, B) ER = A\Y = B\Y, where A, B are arbitrary elements of S. (1) (a) Since for every A ES A\Y = \Y, where ? = B ,the relation R (here and below in (b-d), please type is or is not in the input field below) is reflexive. (b) Given any A, BES, we have that A\Y = B\Y = B\Y= \Y where and hence the relation R is symmetric. (c) For every A, B, CES, (A\Y = B\Y) and (B\Y = C\Y) implies A\Y = \Y, where al= ,and hence the relation R is transitive. (d) Accordingly, by (a,b,c), the relation R is an equivalence relation on S. (11) Find the matrix MR of the relation R (please enter the matrix row-by-row in the six input fields below, when entering each row, seperate the entries by single spaces; understandably, the i-th row/column of the matrix MR must correspond to the i-th set A, in the list of the elements of S given in Eq. (1.1) above): (I)…
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Let n e N. Suppose An = {n,n +1, n +2,...} and T = {0, An}nɛN• (a) Show that T is a topology on N, (b) What are closed sets in t? (c) List the open sets containing the positive integer 6.