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Publication Date:
March 2010
ISSN:
1572-9176
DOI:
10.1515/GMJ.2009.219

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Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.

Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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Dimensional Properties of Generalized Manifolds and Some Properties of Weakly Net-Like Spaces

Ioseb Bakhia1

1Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, 2, University St., Tbilisi 0186, Georgia

Citation Information: Georgian Mathematical Journal. Volume 16, Issue 2, Pages 219–228, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2009.219, March 2010

Publication History:
Received:
2008-05-30
Published Online:
2010-03-11

Abstract

We consider dimensional type functions defined on the class of π-bicompact spaces. Using these functions, the dimensional properties of generalized manifolds are studied. The class of weakly net-like spaces is introduced, which is a natural generalization of net-like spaces in the sense of V. V. Proizvolov and the behavior of this class is studied in the case of (monotone, open) mappings of special type. Generalizations of V. V. Proizvolov's theorems are obtained for weakly net-like spaces.

Key words and phrases:: Dimension; Brouwer's theorem; net-like space; weakly net-like space

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