p-regular Cauchy completions

p-REGULAR CAUCHY COMPLETIONS

This paper gives a further development of p-regular completion theory, including a study ofp-regular Reed completions, the role of diagonal axioms, and the relationship between p-regular and p-topological completions.

p-TOPOLOGICAL CAUCHY COMPLETIONS

The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular,p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and onl...

Cauchy Completions of Mv-algebras

An MV-convergence is a convergence on an MV-algebra which renders the operations continuous. We show that such convergences on a given MV-algebra A are exactly the restrictions of the bounded `-convergences on the abelian `-group in which A appears as the unit interval. Thus the theory of `-convergence and Cauchy structures transfers to MV-algebras. We outline the general theory, and then apply...

Invertible and regular completions of operator matrices

Completions of P-matrix patterns

A list of positions in an n × n real matrix (a pattern) is said to have P-completion if every partial P-matrix that specifies exactly these positions can be completed to a P-matrix. We extend work of Johnson and Kroschel [JK] by proving a larger class of patterns has Pcompletion, including any 4 × 4 pattern with eight or fewer off-diagonal positions. We also show that any pattern whose digraph ...