Category:Definitions/Cohomology Groups

This category contains definitions related to Cohomology Groups.
Related results can be found in Category:Cohomology Groups.

Let $X = \struct {S, \tau}$ be a topological space.

Let $n \in \Z_{\ge 0}$ be a non-negative integer.

Let $f: X \to Y$ denote a continuous mapping from $X$ to another topological space $Y$.

The cohomology groups $\map {H^n} X$ of $X$ are variants of the homology groups of $X$, but with the characteristic property that, given $f: X \to Y$, the corresponding homeomorphisms $f^*$ run from $\map {H_n} Y$ to $\map {H^n} X$ rather than the other way round.