Why don't we define neighbourhoods to be open sets?
84104
Definition of neighborhood and open set in topology
101504
An open ball is an open set
151950
Why is indiscrete topology unmetrizable?
15480
Open set in a metric space is union of closed sets
106944
Is the set defined by y=sin(1/x) open or closed?
115625
Intersection of two open dense sets is dense
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
79424
Don't understand proof that interior of a set is open
16654
Unions and Intersections of Open Sets are Open
44623
Closed set as a countable intersection of open sets
158155
Is set of isolated points of S closed?
133633
A question about path-connected and arcwise-connected spaces
49220
Open Sets of $\mathbb{R}^1$ and axiom of choice
40232
What do we mean when we say "Let $x$ be an element of the set $\mathbb{R}$"?
125233
Why is an open interval not a compact set?
132095
Motivation for the term "separable" in topology
152193
The intersection of a closure with an open set