nLab CW approximation
Contents Context Homotopy theory homotopy theory, (∞,1)-category theory, homotopy type theory flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed… models: topological, simplicial, localic, … see also algebraic topology Introductions Definitions Paths and cylinders Homotopy groups Basic facts Theorems Topology topology (point-set topology, point-free topology) see also differential topology, algebraic topology, functional analysis and topological homotopy theory Introduction Basic concepts
open subset, closed subset, neighbourhood
topological space, locale
base for the topology, neighbourhood base
finer/coarser topology
closure, interior, boundary
separation, sobriety
continuous function, homeomorphism
uniformly continuous function
embedding
open map, closed map
sequence, net, sub-net, filter
convergence
categoryTop Universal constructions Extra stuff, structure, properties
nice topological space
metric space, metric topology, metrisable space
Kolmogorov space, Hausdorff space, regular space, normal space
sober space
compact space, proper map sequentially compact, countably compact, locally compact, sigma-compact, paracompact, countably paracompact, strongly compact
compactly generated space
second-countable space, first-countable space
contractible space, locally contractible space
connected space, locally connected space
simply-connected space, locally simply-connected space
cell complex, CW-complex
pointed space
topological vector space, Banach space, Hilbert space
topological group
topological vector bundle, topological K-theory
topological manifold Examples
empty space, point space
discrete space, codiscrete space
Sierpinski space
order topology, specialization topology, Scott topology
Euclidean space
cylinder, cone
sphere, ball
circle, torus, annulus, Moebius strip
polytope,...