In mathematics, Moore space may refer to: Moore space (algebraic topology) Moore space (topology), a regular, developable topological space....

In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of homotopy theory, in the sense that it has only one nonzero homology (rather than homotopy) group. == Formal definition == Given an abelian group G and an integer n ≥ 1, let X be a CW complex such that H n ( X ) ≅ G {\displaystyle H_{n}(X)\cong G} and...

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 neighbourhoods, and any closed set and any point in its complement can be separated by neighbourhoods. (X is a regular Hausdorff space.) There is a countable collection of open covers of X, 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...

In algebraic topology, universal coefficient theorems establish relationships between homology groups (or cohomology groups) with different coefficients. For instance, for every topological space X, its integral homology groups: Hi(X; Z)completely determine its homology groups with coefficients in A, for any abelian group A: Hi(X; A)Here Hi might be the simplicial homology, or more generally the singular homology: the result itself is a pure piece of homological algebra about chain complexes of free abelian groups. The form of the result is that other coefficients A may be used, at the cost...