General Topology

← Back to Domain-Specific Abstractions by Domain

17 domain-specific abstractions whose origin domain is General Topology.

• Adherent point — A point every neighborhood of which intersects a selected subset, equivalently a member of that subset's closure.
• Development (topology) — A countable sequence of open covers whose stars at each point form a neighborhood base, characterizing developable spaces.
• Discrete space — A topological space in which every subset is open, equivalently every point is isolated and the topology is the full power set.
• Extremally disconnected space — A topological space in which the closure of every open set is open.
• Filters in topology — A set-family formalism that characterizes convergence, continuity, closure, compactness, and limits in arbitrary topological spaces without relying on sequences.
• First-countable space — A topological space in which every point has a countable neighborhood basis.
• H-closed space — A Hausdorff topological space that is closed in every Hausdorff space in which it embeds as a subspace.
• Isolated point — A point of a subset having a neighborhood that contains no other point of that subset.
• Locally Hausdorff space — A topological space in which every point has a neighborhood that is Hausdorff in its subspace topology, allowing locally unique limits while global point separation can still fail.
• Metrizable space — A topological space whose open sets are exactly those generated by some metric on its underlying set.
• Moore space (topology) — A regular Hausdorff topological space possessing a countable development of open covers that locally refines every neighborhood.
• Overlapping interval topology — A topology on the interval minus-one to one generated by left and right half-open intervals whose overlap produces a standard counterexample with distinctive separation properties.
• Saturated set (intersection of open sets) — A subset of a topological space equal to the intersection of all open sets containing it, equivalently an upper set for the specialization preorder.
• Semiregular space — A topological space whose regular open sets form a base for its topology.
• Supercompact space — A topological space possessing a subbase for which every subbasic open cover has a subcover of at most two members, a strong cover property implying compactness and preserved under products.
• Uniformizable space — A topological space whose topology is induced by at least one uniform structure, equivalently a completely regular space under the stated separation convention.
• Wallman compactification — Embed a T1 space densely into a compact space whose points are maximal centered families of closed sets and whose closed subbasis records membership in each original closed set.