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--- math104-s21:hw7 [2021/03/05 23:48]
pzhou
+++ math104-s21:hw7 [2022/01/11 18:31] (current)
24.253.46.239 ↷ Links adapted because of a move operation
@@ Line 1: / Line 1: @@
 ====== HW 7 ======
-This week we discussed continuity of maps, the three equivalent definitions of continuity. Then on Tuesday, after we reviewed some topologies for metric space, we showed that continuous maps sends a compact set to compact set.
+On Tuesday, we discussed continuity of maps, the three equivalent definitions of continuity. Then on Thursday after we reviewed some topologies for metric space, we showed that continuous maps sends a compact set to compact set.
  $\gdef\In\subset$
-Warm up: (no submission required)
+===== Warm up: =====
+no submission required
 . Let  $f: X \to Y$  be a map between metric spaces. Check if the following statements are true or not. If you think the statement is false, give some counter example. If you think the statement is true, give some reasoning.
@@ Line 16: / Line 18: @@
 . Let  $f: (0, \infty) \to \R$  be a map given by  $f(x) = \sin(1/x)$ , prove that  $f$  is continuous. You may use that  $\sin(x)$  is a continuous function.
-Homework:
+===== Homework: =====
-{{ :math104:rudin_ch4.pdf |Rudin Ch 4}} p99: 1, 2, 4, 6, 7
+{{ math104-s21:rudin_ch4.pdf |Rudin Ch 4}} p99: 1, 2, 4, 6, 7, 18
+Note that for problem 18, you only need to prove that  $f$  is continuous at every irrational point (since we haven't discuss what is a simple discontinuity.)

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