algebraic topology, Alexander–Spanier cohomology is a cohomology theory for topological spaces. It was introduced by James W. Alexander (1935) for the special...

to define cohomology for topological spaces (such as singular cohomology, Čech cohomology, Alexander–Spanier cohomology or sheaf cohomology). (Here sheaf...

known for the Alexander-Spanier cohomology theory Graham Spanier (born 1948), former president of Penn State University Muggsy Spanier (1906–1967), American...

Spanier–Whitehead duality and Alexander–Spanier cohomology, and wrote what was for a long time the standard textbook on algebraic topology (Spanier 1981)...

cohomology. Alexander-Spanier cohomology Čech cohomology Spanier, Edwin H. (1966). Algebraic topology. Springer. p. 289. ISBN 978-0387944265. Spanier...

Rham cohomology. If X is compact Hausdorff, then Čech cohomology (with coefficients in a discrete group) is isomorphic to Alexander-Spanier cohomology. For...

theorem Cohomology List of cohomology theories Cocycle class Cup product Cohomology ring De Rham cohomology Čech cohomology Alexander–Spanier cohomology Intersection...

sphere Alexander polynomial Alexander cochain Alexander–Spanier cohomology Alexander duality Alexander's trick Staff. A COMMUNITY OF SCHOLARS: The Institute...

enters naturally on one side of the duality; see for example Alexander–Spanier cohomology. Bredon, Sheaf Theory (2nd edition, 1997) gives these definitions...

EO2. Alexander–Spanier cohomology Algebraic K-theory BRST cohomology Cellular homology Čech cohomology Crystalline cohomology De Rham cohomology Deligne...

makes no use of sheaves. This treatment, however, applied to Alexander–Spanier cohomology with compact supports, as applied to proper maps of locally compact...

{\displaystyle (X^{*})^{*}=X} . Alexander duality implies the following combinatorial analog (for reduced homology and cohomology, with coefficients in any...

Spanier (Ph.D. 1947), mathematician working in algebraic topology; known for his contributions to the development of the Alexander–Spanier cohomology...

respectively. Taking homology and cohomology with respect to an Eilenberg–MacLane spectrum recovers Alexander duality formally. Spanier, Edwin H.; Whitehead, J...

algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a cochain complex. That is, cohomology is defined as the...

abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext). There is a further group...

from other alternative foundations of homology like Cech or Alexander-Spanier cohomology is that it is of particular interest for algebraic geometry since...

sequence holds for a variety of cohomology and homology theories, including simplicial homology and singular cohomology. In general, the sequence holds...

"Isotopy (in topology)", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Spanier, Edwin (December 1994). Algebraic Topology. Springer. ISBN 978-0-387-94426-5...

Deligne–Beilinson cohomology Deligne–Beilinson cohomology delooping degeneracy cycle degree de Rham 1.  de Rham cohomology, the cohomology of complex of differential...

Lecture Notes on Elementary Topology and Geometry, ISBN 0-387-90202-3 Spanier, Edwin H. (1989), Algebraic Topology, Springer, ISBN 0-387-94426-5 Strom...