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In this paper we have considered the multidimensional cosmological implications of a decay law for Λ term that is proportional to βä a , where β is a constant and a is the scale factor of RW-space time. We discuss the cosmological consequences of a model for the vanishing pressure for the case k = 0. It has been observed that such models are compatible with the result of recent observations and cosmological term Λ gradually reduces as the universe expands. In this model Λ varies as the inverse square of time, which matches its natural units. The proper distance, the luminosity distance-redshift, the angular diameter distance-redshift, and look back time-redshift for the model are presented in the frame work of higher dimensional space time. The model of the Freese et al. (Nucl. Phys. B 287, 797 (1987)) for n = 2 is retrieved for the particular choice of A 0 and also Einstein-de Sitter model is obtained for A 0 = 2 3 . This work has thus generalized to higher dimensions the well-know result in four dimensional space time. It is found that there may be significant difference in principle at least, from the analogous situation in four dimensional space time.

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In this paper generalized vector fields are studied. The notion of left invariant vector fields is extended by the use of top spaces. As a result a new kind of dynamics is extrapolated. By the topological properties of topological generalized groups, topological complete semi-dynamical'systems are studied. A method for constructing a complete semi-dynamical system on a generalized coset space is deduced. An application in the genetic space and the whether system are considered.

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