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PROPOSITION 4.8. (1) If {U1, ..., Un} is a collection of closed sets, then JUk is also a closed k=1 set. (2) If {Ua} is a collection of closed sets, then Ua is also a closed set.

PROPOSITION 4.8. (1) If {U1, ..., Un} is a collection of closed sets, then JUk is also a closed k=1 set. (2) If {Ua} is a collection of closed sets, then Ua is also a closed set.

Advanced Engineering Mathematics
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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Can you please simply prove prop 4.8 shown in the image. 

REMARK 4.7. De Morgan's laws state that for an arbitrary union or intersection, (Uv.) -n: (nr.) - аnd n PROPOSITION 4.8. (1) If {U1,.., Un} is a collection of closed sets, then | JUk is also a closed k=1 set. (2) If {Ua} is a collection of closed sets, then NUa is also a closed set.
Transcribed Image Text:REMARK 4.7. De Morgan's laws state that for an arbitrary union or intersection, (Uv.) -n: (nr.) - аnd n PROPOSITION 4.8. (1) If {U1,.., Un} is a collection of closed sets, then | JUk is also a closed k=1 set. (2) If {Ua} is a collection of closed sets, then NUa is also a closed set.
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