Question

what is neighbourhood in set theory???​

Answer 1

Answer:

it is a subset of topological space then a neighbourhood of is a set that includes an open set containing. it follows that a set is a neighbourhood of if and only if it is neighbourhood of all the points in the neighbourhood of a point is just a special case of this defination.

Answer 2

Step-by-step explanation:

One defines a topology on a set by specifying the open sets.

Let X be a set. If τ is a family of sets with the following properties, it is called a topology.

X and ∅ are in τ

Any (possibly infinite, even uncountably infinite) union of sets in τ is in τ.

The intersection of any finite number of elements of τ is in τ.

We call the sets in τ the open sets. You can see that the collection of open sets in, for example, R2 has exactly this set of properties.

A neighborhood of a set S is a set P that contains an open set U so S⊂U⊂P.

Hope it helps⏩⏩