Čech Cohomology with Coefficients in a Topological Abelian Group
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 60552307X | ||
| 003 | CHVBK | ||
| 005 | 20210128100748.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10958-015-2601-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2601-4 | ||
| 245 | 0 | 0 | |a Čech Cohomology with Coefficients in a Topological Abelian Group |h [Elektronische Daten] |c [L. Mdzinarishvili, L. Chechelashvili] |
| 520 | 3 | |a Anordinary Čech cohomology H ⌣ ∗ X G $$ {\overset{\smile }{H}}^{\ast}\left(X,G\right) $$ is defined for an arbitrary space X, and the group of coefficients G is assumed to be an Abelian group. On the category A C of compact pairs (X,A), an ordinary Čech cohomology satisfies the continuity axiom (see [1, Theorem 3.1.X]), i.e., we have the isomorphism H ⌣ * X A G ≈ lim → H ⌣ * X m A m G , $$ {\overset{\smile }{H}}^{*}\left(X,A,G\right)\approx \underrightarrow{ \lim }{\overset{\smile }{H}}^{*}\left({X}_m,{A}_m,G\right), $$ where X A = lim ← X m A m , X m A m ∈ A C $$ \left(X,A\right)=\underleftarrow{ \lim}\left({X}_m,{A}_m\right),\left({X}_m,{A}_m\right)\in {A}_C $$ Therefore, an ordinary Čech cohomology is called a continuous cohomology. In the present paper, using a continuous singular cohomology (see [3]), we define a Čech cohomology H ⌣ ∗ X A G $$ {\overset{\smile }{H}}^{\ast}\left(X,A,G\right) $$ with coefficients in an arbitrary topological Abelian group G. We show that the defined cohomology satisfies the continuity axiom. This cohomology is investigated relative to a group of coefficients. In particular, given an inverse sequence of covering projections, a Čech cohomology with coefficients in the inverse limit of this sequence is isomorphic to the inverse limit of a sequence of Čech cohomologies in groups that are elements of the given sequence. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 700 | 1 | |a Mdzinarishvili |D L. |u Georgian Technical University, Tbilisi, Georgia |4 aut | |
| 700 | 1 | |a Chechelashvili |D L. |u Georgian Technical University, Tbilisi, Georgia |4 aut | |
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 211/1(2015-11-01), 40-57 |x 1072-3374 |q 211:1<40 |1 2015 |2 211 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2601-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2601-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mdzinarishvili |D L. |u Georgian Technical University, Tbilisi, Georgia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Chechelashvili |D L. |u Georgian Technical University, Tbilisi, Georgia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 211/1(2015-11-01), 40-57 |x 1072-3374 |q 211:1<40 |1 2015 |2 211 |o 10958 | ||