Displaying similar documents to “Cardinalities and ranks of π -bases in topological spaces”

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that rank ( P * A Q ) = rank ( P * A ) + rank ( A Q ) - rank ( A ) , where A is idempotent, [ P , Q ] has full row rank and P * Q = 0 . Some applications of the rank formula to generalized inverses of matrices are also presented.

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

The rank of the diagonal and submetrizability

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2006)

Commentationes Mathematicae Universitatis Carolinae

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Several topological properties lying between the submetrizability and the G δ -diagonal property are studied. We are mostly interested in their relationship to each other and to the submetrizability. The first example of a Tychonoff space with a regular G δ -diagonal but without a zero-set diagonal is given. The same example shows that a Tychonoff separable space with a regular G δ -diagonal need not be submetrizable. We give a necessary and sufficient condition for submetrizability of a regular...