# Consistent solution of Markov's problem about algebraic sets

@article{Sipacheva2006ConsistentSO, title={Consistent solution of Markov's problem about algebraic sets}, author={Ol'ga V. Sipacheva}, journal={arXiv: Group Theory}, year={2006} }

It is proved that the continuum hypothesis implies the existence of a group M containing a nonalgebraic unconditionally closed set, i.e., a set which is closed in any Hausdorff group topology on M but is not an intersection of finite unions of solution sets of equations in M.

7 Citations

#### References

SHOWING 1-10 OF 14 REFERENCES

A remark on a countable nontopologized group

- Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 3, p. 103 (1980); The Geometry of Defining Relations in Groups (Nauka, Moscow, 1989; Klüwer, Dordrecht, 1991).
- 1980

On unconditionally closed sets

- Amer. Math. Soc. Transl
- 1950

Three papers on topological groups: I. On the existence of periodic connected topological groups. II. On free topological groups. III. On unconditionally closed sets

- Amer. Math. Soc. Transl. 30 (1950).
- 1950

On unconditionally closed sets

- Mat. Sb. 18(60) (1), 3–26 (1946).
- 1946

On unconditionally closed sets Three papers on topological groups: I. On the existence of periodic connected topological groups. II. On free topological groups

- Mat. Sb
- 1946

On unconditionally closed sets

- C. R. (Doklady) Acad. Sci. URSS (N.S.) 44, 180–181 (1944).
- 1944