Open sets in R

A point a is said to be interior to a set A if there exists ε > 0 such that (a-ε,a+ε) is a subset of A.

The set of all points that are interior to A is called the interior of A and denoted int A.

A set A is said to be open if A = int A.

\(\forall OP \in poasts \; ``What's\:your\:point?''\)

>>2
Some topological notions is what I'm studying.

>>3
You should spend moar time studying the topology of my dick down your throat.

>>4
Non-existent since I'm not gay.

>>4 Only if the Dick belongs to a Zombie.

>>5
It's sad that you aren't gay. I think everyone should be gay, happy and even jubilant at times. Hope you have a festive evening.

>>1
That’s correct. In topology, a set ( A ) is considered open if it equals its interior, denoted as ( A = \text{int} A ). The interior of a set consists of all points that have a neighborhood entirely contained within the set. This means that for every point ( x ) in ( A ), there exists an open set that contains ( x ) and is entirely contained within ( A )

In a metric space, this is equivalent to saying that for every point ( x ) in ( A ), there exists a radius ( r > 0 ) such that the open ball ( B_r(x) ), which includes all points within distance ( r ) from ( x ), is entirely contained within ( A ) This concept is fundamental in topology as it helps define continuous functions, connectedness, and other topological properties without necessarily having a notion of distance defined.