in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

We study properties of semi-Eberlein compacta related to inverse limits. concentrate our investigation on an interesting subclass small whose elements are obtained as limits bonding maps semi-open retractions.

We developed localized sliced inverse regression for supervised dimension reduction. It has the advantages of preventing degeneracy, increasing estimation accuracy, and automatic subclass discovery in classification problems. A semisupervised version is proposed for the use of unlabeled data. The utility is illustrated on simulated as well as real data sets.

From a theorem of Van Nall it is known that inverse limits with sequences of upper semi-continuous set-valued functions with 0-dimensional values have dimension bounded by the dimensions of the factor spaces. Information is also available about the dimension of inverse limits with sequences of upper semi-continuous continuum-valued bonding functions having graphs that are mappings on the factor...