Exercise 5. a) Suppose X is a Hausdorff space, and let Cn+1 C Cn CX be a non-increasing sequence of compact connected subsets. Show that the intersection neN Cn is connected. b) Find a non-increasing sequence of closed connected subsets Fn+1 C F C R² such that neN Fn is not connected. c) Show that any non-increasing sequence of connected subsets In+1 C In CR has a connected intersection EN In.
Exercise 5. a) Suppose X is a Hausdorff space, and let Cn+1 C Cn CX be a non-increasing sequence of compact connected subsets. Show that the intersection neN Cn is connected. b) Find a non-increasing sequence of closed connected subsets Fn+1 C F C R² such that neN Fn is not connected. c) Show that any non-increasing sequence of connected subsets In+1 C In CR has a connected intersection EN In.
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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