Euclidean metric) The metric
d
((
x
1
,x
2
)
,
(
y
1
,y
2
)) =
?
(
x
1
?
x
2
)
2
+ (
y
1
?
y
2
)
2
on
R
2
generates the standard (product) topology on
R
2
.
70.2K
Verified Solution
Link Copied!
Question
Advance Math
Euclidean metric) The metric
d
((
x
1
,x
2
)
,
(
y
1
,y
2
)) =
?
(
x
1
?
x
2
)
2
+ (
y
1
?
y
2
)
2
on
R
2
generates the standard (product) topology on
R
2
.
Answer & Explanation
Solved by verified expert
4.1 Ratings (631 Votes)
The given metric isFirst we prove that the metric topology is contained in theproduct topology on Let be a point in and be an open set of metric topology
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: Zin AI - Your personal assistant for all your inquiries!
