2019
Том 71
№ 8

All Issues

Savkin V. I.

Articles: 4
Brief Communications (Russian)

A criterion for Banach manifolds to be finite-dimensional

Savkin V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1712–1713

We extend the results obtained in [1] to the case of arbitrary Banach spaces and manifolds. We give an example of a continuous bijective mapping with discontinuous inverse which acts in a Banach space and differs from the identical mapping only in an open unit ball. A criterion for a Banach manifold to be finite-dimensional is established in terms of the continuity of inverse operators.

Article (Ukrainian)

A criterion for Banach manifolds with a separable model to be finite-dimensional

Savkin V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1099–1103

We give an example of a continuous bijective mapping with a discontinuous inverse which acts in a separable Banach space and differs from the identical mapping only in an open unit ball. A criterion for Banach manifolds with a separable model to be finite-dimensional is established in terms of the continuity of inverse operators.

Article (Ukrainian)

Continuity of maps inverse to quadratic operator polynomials

Petunin Yu. I., Savkin V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 11. - pp. 1512–1521

Article (Ukrainian)

Convergence generated by analytic functionals, and isomorphism of algebras of analytic functions

Petunin Yu. I., Savkin V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 799–803