is pseudocompact and weakly countably compact. Countably locally finite A collection of subsets of a space X is countably locally finite (or σ-locally finite) if it is the union of a countable collection of locally finite collections of subsets of X. Cover A collection of subsets of a space is a cover (or covering) of that space if the union of the collection is the whole space. Covering See Cover. Cut point If X is a connected space with more than one point, then a point x of X is a cut point if the subspace X − {x} is disconnected. 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 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. 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 ℵ0 is a separable space. 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. Development A countable collection of open covers 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 from C. 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 → 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 if every subset of X is open. We say that