general metrizable space

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• Completely metrizable space — In mathematics, a completely metrizable space (complete topological space or topologically complete space) is a topological space (X, T) for which there exists at least one metric d on X such that (X, d) is a complete metric space and d induces… …   Wikipedia

• Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

• Space-filling curve — 3 iterations of a Peano curve construction, whose limit is a space filling curve. In mathematical analysis, a space filling curve is a curve whose range contains the entire 2 dimensional unit square (or more generally an N dimensional hypercube) …   Wikipedia

• Moore space (topology) — In mathematics, more specifically point set topology, a Moore space is a developable regular Hausdorff space. Equivalently, a topological space X is a Moore space if the following conditions hold: Any two distinct points can be separated by… …   Wikipedia

• Separable space — In mathematics a topological space is called separable if it contains a countable dense subset; that is, there exists a sequence { x n } {n=1}^{infty} of elements of the space such that every nonempty open subset of the space contains at least… …   Wikipedia

• Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… …   Wikipedia

• Polish space — In mathematics, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively… …   Wikipedia

• Completely uniformizable space — In mathematics, a topological space (X, T) is called completely uniformizable (or Dieudonné complete or topologically complete) if there exists at least one complete uniformity that induces the topology T. Some authors additionally require X to… …   Wikipedia

• Uniformizable space — In mathematics, a topological space X is uniformizable if there exists a uniform structure on X which induces the topology of X . Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology… …   Wikipedia

• Uniform space — In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and… …   Wikipedia

• Sequential space — In topology and related fields of mathematics, a sequential space is a topological space that satisfies a very weak axiom of countability. Sequential spaces are the most general class of spaces for which sequences suffice to determine the… …   Wikipedia