List of general topology topics
This is a list of general topology topics.
Basic concepts
Limits
- Limit point
- Net (topology)
- Filter (topology)
- Ultrafilter
Topological properties
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
- Sequential space
- First-countable space
- Second-countable space
- Separable space
- Lindelöf space
- Sigma-compact space
Connectedness
Topological constructions
- Direct sum and the dual construction product
- Subspace and the dual construction quotient
- Topological tensor product
Examples
- Discrete space
- Trivial topology
- Cofinite topology
- Finer topology
- Product topology
- Quotient space
- Unit interval
- Continuum (topology)
- Extended real number line
- Long line (topology)
- Sierpinski space
- Cantor set, Cantor space, Cantor cube
- Space-filling curve
- Topologist's sine curve
- Uniform norm
- Weak topology
- Strong topology
- Hilbert cube
- Lower limit topology
- Sorgenfrey plane
- Real tree
- Compact-open topology
- Zariski topology
- Kuratowski closure axioms
- Unicoherent
- Solenoid (mathematics)
Topology and order theory
Combinatorial topology
- Polytope
- Simplex
- Simplicial complex
- CW complex
- Manifold
- Triangulation
- Barycentric subdivision
- Sperner's lemma
- Simplicial approximation theorem
- Nerve of an open covering
Foundations of algebraic topology
Topology and algebra
See also
- Topology glossary
- List of topology topics
- List of geometric topology topics
- List of algebraic topology topics
- Publications in topology
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