jaj•a•person's notes

Tag: m/thm/topology

See Topology MOC.

43 items with this tag.

A bijection is open iff it is closed
A continuous bijection from compact to Hausdorff is a homeomorphism
A map is a homeomorphism iff it is bijective, continuous, and open
A topological space is discrete iff every point is its own connected component
Alexander subbasis theorem
Artin braid group
Borsuk-Ulam theorem
Brouwer's fixed point theorem
Canonical projections are open
Cardinality of a topology
Closed subsets of a compact space are compact
Compact subsets of a Hausdorff space are closed
Conditions for uniqueness of the limit
Connected subspaces of the real line are intervals
Connectedness is transitive
Continuity
Coproduct topology
Every fibre of a local injection is discrete
Hausdorff space
Hausdorffness is preserved by subspaces, products, and coproducts, but not quotients
Heine-Borel theorem
Lattice subgroup
Lift of a map to a covering space
Limit points are limits of convergent subsequences in a first-countable space
Limit points are points contained in the closure of every end piece
Locally path connected spaces have identical connected and path-connected components
Main theorem of connectedness
Metrizable implies Hausdorff
Norms are equivalent iff they induce the same topology
Orbit space of a properly discontinuous group action
Product topology
Proving open map with a subbasis
Quotient topology
Regular monomorphisms in the category of topological spaces
Sequential closedness
Sequential continuity
Sequentially compact space
Subspace topology
The boundary of a ball is not a retract
The continuous image of a compact space is compact
The intersection of nested inhabited Hausdorff-compact sets is inhabited
The intersection of topologies on a fixed set is again a topology
Topological subbasis

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