This is a list of useful examples in general topology, a field of mathematics.
Alexandrov topology
Cantor space
Co-kappa topology
Cocountable topology
Cofinite topology
Compact-open topology
Compactification
Discrete topology
Double-pointed cofinite topology
Extended real number line
Finite topological space
Hawaiian earring
Hilbert cube
Irrational cable on a torus
Lakes of Wada
Long line
Order topology
Lexicographical/dictionary order
Ordinal number topology
Real line
Split interval
Overlapping interval topology
Moore plane
SierpiĆski space
Sorgenfrey line
Sorgenfrey plane
Space-filling curve
Topologist's sine curve
Trivial topology
Unit interval
Zariski topology