On 2005, F. Smarandache generalized the Atanassov’s intuitionistic fuzzy setsto neutrosophic sets. Also, this author and some co-workers introduced the notion of interval neutrosophic set, which is an instance of neutrosophic set and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. We study in this paper relations between i...

R.Devi, K.Balachandran and H.Maki, Generalized α-closed maps and α-generalized closed maps, Indian J. Pure.Appl.Math, 29(1)(1998),37-49. R.Devi, K.Bhuvaneshwari and H.Maki, Weak form on gr-closed sets, where rÎ{a,a*,a**} and the digital plane, Mem. Fac. Sci. Kochi Univ. (Math.), Vol.25(2004), 37-54. R.Devi, S.N.Rajappriya, K.Muthukumaraswamy and H.Maki, -closed sets in topological spaces and d...

In this paper we present a method to improve the learning results for diierent data sets, which earlier were diicult or impossible to learn, and to criticize the map's development during learning. Calculating the generalized fractal dimensions of the data set we choose the map's dimension accordingly for guaranteeing the maps ability of topology preservation. Furthermore we explore diierent sta...

The reasons of the crisis in the contemporary (Riemannian) geometry are discussed. The conventional method of the generalized geometries construction, based on a use of the topology, leads to a overdetermination of the Riemannian geometry. In other words, at the Riemannian geometry construction one uses the needless information (topology), which disagrees with other original axioms. The crisis ...

The properties of the metric topology on infinite and finite sets are analyzed. We answer whether finite metric spaces hold interest in algebraic topology, and how this result is generalized to pseudometric spaces through the Kolmogorov quotient. Embedding into Lebesgue spaces is analyzed, with special attention for Hilbert spaces, `p, and EN .