Topological space
set of points and set of neighborhoods that satisfy axioms relating those points to those neighborhoods
mapping cylinder
sequentially compact space
quotient topological space
topologist's sine curve
regular space
suspension
homogeneous space
totally bounded space
Schwartz space
pointed space
topological vector space
connected space
totally disconnected space
H-space
ringed space
compactly generated space
long line
connected sum
manifold
loop space
universal space
sequential space
cylinder
mapping cone
quotient space of an algebraic stack
join
solenoid
Alexandrov-discrete space
configuration space
Moore space
classifying space
door space
Dunce hat
fixed-point space
locally compact space
rose
relatively compact subspace
Cantor space
separable space
partially ordered space
spectrum of a C*-algebra
topologically stratified space
locally connected space
topological ring
first-countable space