Closure Along an Admissible Subset, Seminormality and $T$-Closedness

THE CATEGORY OF T-CONVERGENCE SPACES AND ITS CARTESIAN-CLOSEDNESS

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

On seminormality

We give an elementary and essentially self-contained proof1 that a reduced ring R is seminormal if and only if the canonical map Pic R → Pic R[X] is an isomorphism, a theorem due to Swan [15], generalizing some previous results of Traverso [16]. By a simple modification of this argument, we obtain a constructive proof, and hence an algorithm [12], associated to a classical proof which is not so...

Compactness, Perfectness, Separation, Minimality and Closedness with Respect to Closure Operators

In this paper, the characterization of closed and strongly closed subobjects of an object in categories of various types of filter convergence spaces is given and it is shown that they induce a notion of closure. Furthermore, each of the notions of compactness, perfectness, separation, minimality and absolute closedness with respect to these two new closure operators are characterized in these ...

T Cell Subset Patterns

HC of an Admissible Set

If A is an admissible set, let HC(A) = {x I x E A and x is hereditarily countable in A}. Then HC(A) is admissible. Corollaries are drawn characterizing the "real parts" of admissible sets and the analytical consequences of admissible set theory. ?1. A transitive set A is admissible if it satisfies pairing, set union, J0-separation and J0-bounding (Platek [7], Barwise [1]). An easy theorem of ZF...