"Nice" Topological Spaces

Basis

Closed

Closure

Compact

Connected

Connected component

Continuous

Convergence

Dense

Discrete topology

Euclidean topology

Every Metric Space is a Topological Space

Extended Real Line

First-countable

Hausdorff

Heine-Borel Theorem

Homeomorphism

Homotopy

Induced Topology

Interior Point

Lindëlof Space

Locally Compact

Locally constant

Loop

Metric Space

Metrizable

Neighbourhood

Notions of Compactness

Open

Paracompact

Path connected

Precompact

Proper

Relatively Compact

Second-countable

Separable

Sequentially Compact

Simply connected

Standard topology

Topological Space

Topology

Totally Bounded

Trivial topology

σ-compact