meaning of open sets in topological space For a topological space $(X,\Omega)$ , $\Omega$ represents open sets of this space. But why are they called open sets and are they the same open sets as normal set theory?

How will naming them closed sets will affect our understanding ?
 A: The name means nothing. The properties are what we care about.
The idea of open sets comes to generalize the open sets on the real line. On the real line we have that the union of open sets is open; the intersection of finitely many open sets is open; and that the whole space and the empty sets are open.
So a topological space is a non-empty set $X$ and a collection of subsets, $\Omega$, which has these properties. It doesn't matter how you call them, it matters how they behave. But then again, if you give them different names from everyone else no one will understand you.
Closed sets, in particular, behave in an opposite way, and the name reflects the fact that convergent sequences (or nets) within a closed set, have their limits inside the closed set. So it is closed under limits, in some sense.
But again, this is just a name. We use it for a while, and then you kinda have to use it if you want to talk to other people. If you ever get stuck on an island you can always call them by a different name.
