Extending Mappings between Posets

ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS

In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mapping...

Contraction Mappings in Fuzzy Quasi-metric Spaces and [0,1]-fuzzy Posets

It is well known that each bounded ultraquasi-metric on a set induces, in a natural way, an [0,1]-fuzzy poset. On the other hand, each [0,1]-fuzzy poset can be seen as a stationary fuzzy ultraquasi-metric space for the continuous t-norm Min. By extending this construction to any continuous t-norm, a stationary fuzzy quasi-metric space is obtained. Motivated by these facts, we present several co...

Monotonic Mappings Invariant Linearisation of Finite Posets

In this paper we describe a novel a procedure to build a linear order from an arbitrary poset which (i) preserves the original ordering and (ii) allows to extend monotonic and antitonic mappings defined over the original poset to monotonic and antitonic mappings over the new linear poset.

Completion of Posets with Projections

Posets with (I;)-indexed projections are triples (D; ; (p i) i2I). They consist of a partially ordered set (D;) and a monotone net (p i) i2I of projections on D with a xed directed index set (I;). In this paper we prove that there is a unique \completion" (b D; b ; (b p i) i2I) of (D; ; (p i) i2I). It is complete with respect to the uniformity induced by the kernels of all b p i. Moreover, it s...

Inductive properties of fixed point sets of mappings on posets and on partially ordered topological spaces