Home > List of general topology topics

1 Basic concepts

• Topological space
• Open set, closed set
  • Clopen set
  • Closure (topology)
  • Boundary (topology), boundary
  • Dense (topology)
  • G-delta set, F-sigma set
• Continuity (topology)
  • Homeomorphism
  • Local homeomorphism
  • Open and closed mapsIn topology, an open map is a function between two topological spaces which maps open sets to open sets. That is, a function f : X → Y is open if for any open set U in X the image f ''U is open in Y''. Likewise, a closed map is a function which maps
  • Germ (mathematics)In mathematics, a germ is an equivalence class of continuous functions from one topological space to another (often from the real line to itself), in which one point x in the domain has been singled out as privileged. Two functions f and g are equivalent
• Base (topology)In mathematics, a base (or basis B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B''. We say that the base generates the topology T''. Bases are useful be, subbaseIn topology, a subbase (or subbasis for a topological space X with topology T is a subcollection B of T such that every open set in T can be written as a union of finite intersections of elements of B''. We say that the subbase generates the topology T an
• Open cover
• Atlas (topology)In topology, an atlas describes how a complicated space is glued together from simpler pieces. Each piece is given by a chart (also known as coordinate chart or local coordinate system . More precisely, an atlas for a complicated space is constructed out

2 Limits

• Limit pointTopology General topology In mathematics, informally speaking, a limit point (or cluster point of a set S in a topological space X is a point x in X that can be "approximated" by points of S other than x as well as one pleases. This concept profitably gen
• Net (topology)
• Filter (topology)
• Ultrafilter

3 Topological properties

3.1 Compactness and Countability

• Compact space
  • Relatively compact subspace
  • Heine-Borel theorem
  • Tychonoff's theorem
  • Finite intersection property
  • Compactification
  • Measure of non-compactness
• Paracompact space
• Locally compact space
• Compactly generated space
• Axiom of countability
• First-countable space
• Second-countable space
• Separable space
• Lindelöf space
• Sigma-compactness