When is the interior of a set empty

The purple curve behaves like a lasso, while the green one can be shrunk to the point where both started. Now both of these notions are very different and not really comparable, but I still hope that my answer helps you. Python Javascript Linux Cheat sheet Contact. What is the difference between an "empty interior" and a "hole" in topology? You can see them in this picture from wikipedia where neither circle can be collapsed while remaining on the surface: The surface of a sphere has no holes: every circle can be shrunk to a point.

Consider for example: The union of the three drawn disks is the set of all points that contained in at least one of the three disks given by the hatched lines. What can we say about empty interior now?

For example: The purple curve behaves like a lasso, while the green one can be shrunk to the point where both started. Tags: Terminology. Related Chemistry - Why "monoxide" but not "diodine"? Chemistry - What is the difference in mosM and mOsm units, if there is any at all? Chemistry - What is the intuition behind 'mol' as a unit 'symbol' Chemistry - What is an ambident substrate? Thus, a finite set cannot be a nbd of any points. Hence, no points of finite non-empty set is an interior point.

Upvote This discussion on Which of the following is correct? Correct answer is option 'A'. Can you explain this answer? The Questions and Answers of Which of the following is correct? If the answer is not available please wait for a while and a community member will probably answer this soon.

You can study other questions, MCQs, videos and tests for Mathematics on EduRev and even discuss your questions like Which of the following is correct? Apart from being the largest Mathematics community, EduRev has the largest solved Question bank for Mathematics.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?

Learn more. Empty interior, equivalent definitions from Munkres. Ask Question. Asked 5 years, 10 months ago. Active 4 years, 3 months ago. Perhaps I am overlooking something obvious, but at any rate unless I see a more specific reference to the suggested result, or a sketch of proof, I would not consider the above question answered.

It's not hard to construct a compact connected LOTS with this property. Almost P-spaces. Chang Il Kim. Korean Math. Ronnie Levy. XXIX, No. Sign up to join this community. The best answers are voted up and rise to the top. Ask Question. Asked 6 years, 7 months ago.