1 Let (X, d) be a metric space such that the intersection of open set and closed set is always open. Suppose that for each set E, there is a closed set F such that FCE. Show that if there is a set J such that J is open and closed, then there is a sequence of set {n} such that J₁ J₂ J3 Ɔ ... and Jn is open and closed, for all n € N.
1 Let (X, d) be a metric space such that the intersection of open set and closed set is always open. Suppose that for each set E, there is a closed set F such that FCE. Show that if there is a set J such that J is open and closed, then there is a sequence of set {n} such that J₁ J₂ J3 Ɔ ... and Jn is open and closed, for all n € 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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Let (X, d) be a metric space such that the intersection of open set
and closed set is always open. Suppose that for each set E, there is a closed
set F such that FC E. Show that if there is a set J such that J is open and
closed, then there is a sequence of set {n} such that J₁ J2 J3 Ɔ ... and
Jn is open and closed, for all n € N.
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