Show that any open subset of R (w std. topology) is a countable union of...
70.2K
Verified Solution
Link Copied!
Question
Advance Math
Show that any open subset of R (w std. topology) is a countable union of open intervals.
What is the objective of this problem and enough to show ?
Answer & Explanation
Solved by verified expert
3.6 Ratings (328 Votes)
Answer First recall that the standard topology of is the topology generated by the basis Thus an open subset in the standard topology is a subset which can be written as union
See Answer
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
