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The First Turkish International Conference on Topology and its Applications
August 2-5, 2000
Istanbul University
Istanbul, Turkey

Organizers
Nurettin Ergun, Mahir Hasanov, Turgut Önder, Cem Tezer, Murat Tuncali, Stephen Watson

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Cech and Singular Homology Locally Connectivity
by
Umed H. Karimov
Institute of Mathematics, Ul. Ainy, 299, Dushanbe (734063),TAJIKISTAN

Let H*S (resp. \check H*) be singular homology (resp. Cech cohomology) groups with integer coefficients. Finite-dimensional space X is called homology (cohomology) locally connected (abbreviated HLC, respectively clc space) if for every point x in X and for every neighborhood Ux there exist neighborhood Vx subset Ux such that the inclusion-induced homomorphism H*S (Vx, {x}) --> H*S (Ux, {x}) (resp. \check H* (Ux, {x}) --> \check H*(Vx, {x})) is zero.

G.E. Bredon has showed that there exist compact normal clc spaces which are not HLC spaces ([1], p.130, 131).

Main result of the report is:

Theorem. There exist 2-dimensional compact metrizable clc space X which is not HLC space.

References

[1] G. E. Bredon, Sheaf Theory, Springer-Verlag, New York, 1997.

Date received: June 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeh-18.