Nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. In this work we introduce this concept in an $S$-poset, aposet with an action of a posemigroup $S$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $S$-net. Using $S$-nets and itsconvergency we...

and Applied Analysis 3 In this paper, L always denotes a complete residuated lattice unless otherwise stated, and L denotes the set of all L-subsets of a nonempty set X. For all A,B ∈ L , we define A ∩ B x A x ∧ B x , A ∪ B x A x ∨ B x , A ∗ B x A x ∗ B x , A −→ B x A x −→ B x . 2.1 Then L, ∗, → ,∨,∧, 0, 1 is also a complete residuated lattice. If no confusion arises, we always do not discrimin...

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

Poset game, which includes some famous games. e.g., Nim and Chomp as sub-games, is an important two-player impartial combinatorial game. The rule of the game is as follows: For a given poset (partial ordered set), each player intern chooses an element and the selected element and it’s descendants (elements succeeding it) are all removed from the poset. A player who choose the last element is th...

Let R be a non empty poset and let A, B be many sorted sets indexed by R. One can check that every many sorted relation between A and B which is os-compatible is also order-sorted. Let R be a non empty poset and let A be a many sorted set indexed by the carrier of R. An order sorted relation of A is an order sorted relation of A, A. Let S be an order sorted signature and let U1 be an order sort...

For a countable ultrahomogeneous graph G = 〈G, ρ〉 let P(G) denote the collection of sets A ⊂ G such that 〈A, ρ ∩ [A]〉 ∼= G. The order types of maximal chains in the poset 〈P(G) ∪ {∅},⊂〉 are characterized as: (I) the order types of compact sets of reals having the minimum nonisolated, if G is the Rado graph or the Henson graph Hn, for some n ≥ 3; (II) the order types of compact nowhere dense set...

For q ∈ C generic, we give an algorithmic construction of an ordered bijection between the set of H-primes of Oq (Mn(C)) and the sub-poset S of the (reverse) Bruhat order of the symmetric group S2n consisting of those permutations that move any integer by no more than n positions. Further, we describe the permutations that correspond via this bijection to rank t H-primes. More precisely, we est...

Results of R. Stanley and M. Masuda completely characterize the hvectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vectors. We also present new methods for constructing poset balls with specific h-...