List of general topology topics
This is a list of general topology topics, by Wikipedia page.
Basic concepts
- Topological space
- Topological property
- Open set, closed set
- Clopen set
- Closure (topology)
- Boundary (topology)
- Dense (topology)
- G-delta set, F-sigma set
- closeness (mathematics)
- neighbourhood (mathematics)
- Continuity (topology)
- Base (topology), subbase
- Open cover
- Covering space
- Atlas (topology)
Limits
- Limit point
- Net (topology)
- Filter (topology)
- Ultrafilter
Topological properties
- Baire category theorem
- Nowhere dense
- Baire space
- Banach–Mazur game
- Meagre set
- Comeagre set
Compactness and countability
Connectedness
Separation axioms
- T0 space
- T1 space
- Hausdorff space
- Completely Hausdorff space
- Regular space
- Tychonoff space
- Normal space
- Urysohn's lemma
- Tietze extension theorem
- Paracompact
- Separated sets
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)
Metric spaces
- Metric topology
- Manhattan distance
- Ultrametric space
- P-adic numbers, p-adic analysis
- Open ball
- Bounded subset
- Pointwise convergence
- Metrization theorems
- Complete space
- Cauchy sequence
- Banach fixed point theorem
- Polish space
- Hausdorff distance
- Intrinsic metric
- Category of metric spaces
Topology and order theory
Dimension 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
- Topological algebra
- Topological group
- Topological ring
- Topological vector space
- Topological module
- Topological abelian group
- Properly discontinuous
- Sheaf space
gollark: When have you needed that?
gollark: It is, because nobody actually needs to print `y\n` at 120GB/s. In fact, you're not even PRINTING it, just... counting and devnulling it.
gollark: They were able to reach 120GB/s, vs 120MB/s with the naive implementation or 12GB/s with the GNU yes one.
gollark: https://www.reddit.com/r/unix/comments/6gxduc/how_is_gnu_yes_so_fast/
gollark: The current state of the art in "printing constant text really fast" is probably contained in a reddit thread talking about the performance of GNU yes.
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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