Editing Glossary of general topology (section)

== D ==
;δ-cluster point, δ-closed, δ-open: A point ''x'' of a topological space ''X'' is a δ-cluster point of a subset ''A'' if <math>A \cap \operatorname{Int}_X\left( \operatorname{Cl}_X(U) \right) \neq \emptyset</math> for every open neighborhood ''U'' of ''x'' in ''X''.  The subset ''A'' is δ-closed if it is equal to the set of its δ-cluster points, and δ-open if its complement is δ-closed.{{sfn|Hart|Nagata|Vaughan|2004|pp=8–9}}

;[[Dense set]]: A set is dense if it has nonempty intersection with every nonempty open set. Equivalently, a set is dense if its closure is the whole space.

;[[Dense-in-itself]] set: A set is dense-in-itself if it has no [[isolated point]].

;Density: the minimal cardinality of a dense subset of a topological space.  A set of density ℵ<sub>0</sub> is a [[separable space]].<ref>Nagata (1985) p.104</ref>

;Derived set: If ''X'' is a space and ''S'' is a subset of ''X'', the derived set of ''S'' in ''X'' is the set of limit points of ''S'' in ''X''.

;Developable space: A topological space with a [[Development (topology)|development]].<ref name=ss163/>

;[[Development (topology)|Development]]: A [[countable set|countable]] collection of [[open cover]]s of a topological space, such that for any closed set ''C'' and any point ''p'' in its complement there exists a cover in the collection such that every neighbourhood of ''p'' in the cover is [[disjoint sets|disjoint]] from ''C''.<ref name=ss163/>

;Diameter: If (''M'', ''d'') is a metric space and ''S'' is a subset of ''M'', the diameter of ''S'' is the [[supremum]] of the distances ''d''(''x'', ''y''), where ''x'' and ''y'' range over ''S''.

;Discrete metric: The discrete metric on a set ''X'' is the function ''d'' : ''X'' × ''X'' &nbsp;→&nbsp; '''[[real number|R]]''' such that for all ''x'', ''y'' in ''X'', ''d''(''x'', ''x'') = 0 and ''d''(''x'', ''y'') = 1 if ''x'' ≠ ''y''. The discrete metric induces the discrete topology on ''X''.

;[[Discrete space]]: A space ''X'' is [[discrete space|discrete]] if every subset of ''X'' is open. We say that ''X'' carries the '''discrete topology'''.<ref name=ss41>Steen &amp; Seebach (1978) p.41</ref>

;[[Discrete topology]]: See '''[[discrete space]]'''.

;Disjoint union topology: See '''Coproduct topology'''.

;[[Dispersion point]]: If ''X'' is a connected space with more than one point, then a point ''x'' of ''X'' is a dispersion point if the subspace ''X'' − {''x''} is hereditarily disconnected (its only connected components are the one-point sets).

;Distance: See '''[[metric space]]'''.

;[[Dowker space]]

;[[Dunce hat (topology)]]