- How can you tell if something is closed?
- What makes a set closed?
- How can we find measure of open set and closed set?
- Can an open set be closed?
- Is r2 a closed set?
- Is Z an open set?
- Can sets be open and closed?
- Is RN a closed set?
- Is a B a closed set?
- Is a set either open or closed?

A closed set is a set that contains its boundary points. If we think of an interval on real line, such as (0,1) and [0,1], the first interval is open and the second one is closed.

In mathematics, a set is closed under an operation if performing that operation on members of the set always produces a member of that set. For example, the positive integers are closed under addition, but not under subtraction: 1 − 2 is not a positive integer even though both 1 and 2 are positive integers.

A subset E ⊂ Rd is open if for every x ∈ E there exists r > 0 with Br(x) ⊂ E. By definition, a set is closed if its complement is open.

Sets can be open, closed, both, or neither. (A set that is both open and closed is sometimes called "clopen.") The definition of "closed" involves some amount of "opposite-ness," in that the complement of a set is kind of its "opposite," but closed and open themselves are not opposites.

But R2 also contains all of its limit points (why?), so it is closed.

Therefore, Z is not open.

Sets can be open, closed, both, or neither. (A set that is both open and closed is sometimes called "clopen.") The definition of "closed" involves some amount of "opposite-ness," in that the complement of a set is kind of its "opposite," but closed and open themselves are not opposites.

Hence, both Rn and ∅ are at the same time open and closed, these are the only sets of this type. Furthermore, the intersection of any family or union of finitely many closed sets is closed. Note: there are many sets which are neither open, nor closed.

The sets [a,b], (−∞,a], and [a,∞) are closed. Indeed, (−∞,a]c=(a,∞) and [a,∞)c=(−∞,a) which are open by Example 2.6. 1.

If x∈V and V is open, then we say that V is an open neighborhood of x (or sometimes just neighborhood). Intuitively, an open set is a set that does not include its “boundary.” Note that not every set is either open or closed, in fact generally most subsets are neither. The set [0,1)⊂R is neither open nor closed.

How long can you keep sweet and sour sauce?

Does gold react with sweat?

Is suspension the same as fired?

One watt (W) is the rate at which work is done when one ampere (A) of current flows through an electrical potential difference of one volt (V).

So basically super Shenron is omnipotent and omniscient, he can manipulate time, matter, reality etc but his powers are limited to the imagination of the wisher. You can literally imagine and wish for anything that's impossible. It doesn't mean his creator is stronger than Zeno.