Samiksha Jaiswal (Editor)

List of general topology topics

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This is a list of general topology topics, by Wikipedia page.

Contents

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)
  • Homeomorphism
  • Local homeomorphism
  • Open and closed maps
  • Germ (mathematics)
  • 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

  • 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

  • Connected space

    • 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
  • Locally constant function
  • Trivial topology
  • Cofinite topology
  • Finer topology
  • Product topology
  • Restricted product
  • 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)

    • Uniform spaces

  • Uniform continuity
  • Lipschitz continuity
  • Uniform isomorphism
  • Uniform property
  • Uniformly connected space

    • 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

  • Stone duality
  • Stone's representation theorem for Boolean algebras
  • Specialization (pre)order
  • Sober space
  • Spectral space
  • Alexandrov topology
  • Upper topology
  • Scott topology
  • Scott continuity
  • Lawson topology

    • Descriptive set theory

    Polish Space

    Cantor space

    Dimension theory

  • Inductive dimension
  • Lebesgue covering dimension
  • Lebesgue's number lemma

    • 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

  • Simply connected
  • Semi-locally simply connected
  • Path (topology)
  • Homotopy
  • Homotopy lifting property
  • Pointed space
  • Wedge sum
  • smash product
  • Cone (topology)
  • Adjunction space

    • Topology and algebra

  • Topological algebra
  • Topological group
  • Topological ring
  • Topological vector space
  • Topological module
  • Topological abelian group
  • Properly discontinuous
  • Sheaf space

    • References

    List of general topology topics Wikipedia
    (Text) CC BY-SA


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