In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

This paper is devoted to the investigation of weighted mean topological dimension in dynamical systems. We show that not larger than metric dimension, which generalizes classical result Lindenstrauss and Weiss [16] . also establish relationship between entropy systems, indicates each system with finite or small boundary property has zero dimension.

The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape...

analysis. In Proc. 21st Int. Conf. on Machine Learning, 2004. 5. Ding C., He X., Zha H., and Simon H. Unsupervised learning: self-aggregation in scaled principal component space. Principles of Data Mining and Knowledge Discovery, 6th European Conf., 2002, pp. 112–124. 6. Fiedler M. Algebraic connectivity of graphs. Czech. Math. J., 23:298–305, 1973. 7. Hagen M. and Kahng A.B. New spectral metho...

We present two extensions of the algorithm by Broomhead et al [2] which is based on the idea that singular values that scale linearly with the radius of the data ball can be exploited to develop algorithms for computing topological dimension and for detecting whether data models based on manifolds are appropriate. We present a geometric scaling property and dimensionality criterion that permit ...

Krull dimension measures the depth of the spectrum Spec(R) of a commutative ring R. Since Spec(R) is a spectral space, Krull dimension can be defined for spectral spaces. Utilizing Stone duality, it can also be defined for distributive lattices. For an arbitrary topological space, the notion of Krull dimension is less useful. Isbell [23] remedied this by introducing the concept of graduated dim...