0 like 0 dislike
0 like 0 dislike
A set defined by a local property imply that it is an open set?

2 Answers

0 like 0 dislike
0 like 0 dislike
You should probably cite more of the proof, as is that can be a lot of things. "Based on a local property" is not very precise.

If you mean something like "The underlying space fulfills this property locally, i. e. for each point, we can find a neighbourhood where the property is fulfilled", then you can always choose the local subset (the neighbourhood) open, that follows from the definition of a neighbourhood ("contains an open set that contain the point in question").
0 like 0 dislike
0 like 0 dislike
Going out on a limb, I assume you have a topological (or metric, or normed) space X and the set in question is of the form S={x in X | x has property P}. And that P is a local property in the sense that if x has the property P, then so does every point in a suitable open neighborhood of x. Then this neighborhood would, by definition, be contained in S. And since this is true of every point of S, there is an open neighborhood around every point of S, which is also contained in S. Which makes S open.

Related questions

0 like 0 dislike
0 like 0 dislike
1 answer
MSR_Tlse asked Jun 21
Are the S3/S4 Edexcel Further Maths units useful to become an actuary? Topics include sampling, unbiased and biased estimators, confidence intervals and significance test...
MSR_Tlse asked Jun 21
0 like 0 dislike
0 like 0 dislike
9 answers
HilaryKHarper asked Jun 21
Has anyone successfully guessed on like half of the questions on an exam and still passed?
HilaryKHarper asked Jun 21
0 like 0 dislike
0 like 0 dislike
19 answers
chorleyfc asked Jun 21
What do you do after an exam without instant results?
chorleyfc asked Jun 21
0 like 0 dislike
0 like 0 dislike
26 answers
ShanePaulNeil asked Jun 21
Why is it boring to be an actuary?
ShanePaulNeil asked Jun 21
0 like 0 dislike
0 like 0 dislike
7 answers
alfonsoesparzao asked Jun 21
Using SOA suggested text books to study for an exam
alfonsoesparzao asked Jun 21

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!