Skip to main content
MathOverflow

Return to Question

deleted 5 characters in body; edited tags
Source Link
Mehmet Onat
Mehmet Onat
  • 1.4k
  • 7
  • 12

Suppose that a paracompact space $X$ is the inverse limit of paracompact spaces $X_{i}$ (that is $X=\varprojlim X_{i}$) and $H^{\ast }$ is Alexander-Spanier cohomology (or with closed supports). Then the equality $H^{\ast }\left( X,k\right) =\varinjlim H^{\ast }\left( X_{i},k\right) $ is true? (where $k$ is a field of characteristic zero.)

Suppose that a paracompact space $X$ is the inverse limit of paracompact spaces $X_{i}$ (that is $X=\varprojlim X_{i}$) and $H^{\ast }$ is Alexander-Spanier cohomology (or with closed supports). Then the equality $H^{\ast }\left( X,k\right) =\varinjlim H^{\ast }\left( X_{i},k\right) $ is true? (where $k$ is a field of characteristic zero.)

Suppose that a paracompact space $X$ is the inverse limit of paracompact spaces $X_{i}$ (that is $X=\varprojlim X_{i}$) and $H^{\ast }$ is Alexander-Spanier cohomology with closed supports. Then the equality $H^{\ast }\left( X,k\right) =\varinjlim H^{\ast }\left( X_{i},k\right) $ is true? (where $k$ is a field of characteristic zero.)

Source Link
Mehmet Onat
Mehmet Onat
  • 1.4k
  • 7
  • 12

Continuity of Alexander-Spanier cohomology

Suppose that a paracompact space $X$ is the inverse limit of paracompact spaces $X_{i}$ (that is $X=\varprojlim X_{i}$) and $H^{\ast }$ is Alexander-Spanier cohomology (or with closed supports). Then the equality $H^{\ast }\left( X,k\right) =\varinjlim H^{\ast }\left( X_{i},k\right) $ is true? (where $k$ is a field of characteristic zero.)