The σ1-topology and λ1-topology on s1-quasicontinuous posets

Formal Topology with Posets

On the Möbius Function and Topology of General Pattern Posets

We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on the Möbius function and topology of such pattern posets. We prove our results using a poset fibration based on the embeddings of the poset, where embeddings are representations of occurrences. We show that the Möbius ...

The topology of restricted partition posets

For each composition ~c we show that the order complex of the poset of pointed set partitions Π• ~c is a wedge of β(~c) spheres of the same dimensions, where β(~c) is the number of permutations with descent composition ~c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module S where B is a border strip associated to the composition ~c. We also st...

Topology on Coalgebras

A note on topology of Z-continuous posets

Z-continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of Z-continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a Z-continuous poset is de ned and its properties are explored.