On the MacNeille Completion of the Category of Partially Ordered Topological Spaces

1993 ◽  
Vol 163 (1) ◽  
pp. 281-288 ◽  
Author(s):  
A. Schauerte
Keyword(s):  
Topological Spaces ◽  
Macneille Completion ◽  
Partially Ordered

scholarly journals Fixed Point Theorems of Set-Valued Mappings in Partially Ordered Hausdorff Topological Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shujun Jiang ◽  
Zhilong Li ◽  
Shihua Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Monotone Mappings ◽  
Topological Spaces ◽  
Partially Ordered ◽  
Set Valued Mappings

In this work, several fixed point theorems of set-valued monotone mappings and set-valued Caristi-type mappings are proved in partially ordered Hausdorff topological spaces, which indeed extend and improve many recent results in the setting of metric spaces.

scholarly journals Endpoints inT0-Quasimetric Spaces: Part II

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Collins Amburo Agyingi ◽  
Paulus Haihambo ◽  
Hans-Peter A. Künzi
Keyword(s):  
Complete Lattice ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partial Orders ◽  
Macneille Completion ◽  
Partially Ordered ◽  
Irreducible Elements ◽  
Quasimetric Space

We continue our work on endpoints and startpoints inT0-quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valuedT0-quasimetrics, that is, essentially, to partial orders. For instance, we observe that in a complete lattice the startpoints (resp., endpoints) in our sense are exactly the completely join-irreducible (resp., completely meet-irreducible) elements. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and theq-hyperconvex hull of its naturalT0-quasimetric space.

scholarly journals On the lattice equivalence of topological spaces

1966 ◽  
Vol 6 (4) ◽  
pp. 495-511 ◽  
Author(s):  
P. D. Finch
Keyword(s):  
Topological Space ◽  
Distributive Lattice ◽  
Topological Spaces ◽  
Partially Ordered ◽  
Set Inclusion ◽  
Set Intersection ◽  
Finite Set

A topology on a set X is defined by specifying a family of its subsets which has the properties (i) arbitrary set intersections of members of belong to , (ii) finite set unions of members of belong to and (iii) the empty set □ and the set X each belong to . The members of are called the closed subsets of X. If X is any subset of X then denotes the closure of X, that is, the set intersection of all closed subsets which contain X, however when X = {x} contains one point only we will denote by . The pair (X, ) is called a topological space or, in what follows, a T-space. By a T-lattice we mean a complete distributive lattice of sets in which arbitrary g.l.b. means arbitrary set intersection, finite l.u.b. means finite set union and which contains the empty set □ It is well-known, for example Birkhoff [1], that if (X, ) is a T-space and the members of are partially ordered by set inclusion then is a T-lattice.

scholarly journals Extensions of G-posets and Quillen's complex

1994 ◽  
Vol 57 (1) ◽  
pp. 60-75 ◽  
Author(s):  
Yoav Segev ◽  
Peter Webb
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Exact Sequence ◽  
Partially Ordered Sets ◽  
Topological Spaces ◽  
Ordered Sets ◽  
Wedge Product ◽  
Partially Ordered ◽  
Steinberg Module ◽  
A Finite Group

AbstractWe develop techniques to compute the homology of Quillen's complex of elementary abelian p-subgroups of a finite group in the case where the group has a normal subgroup of order divisible by p. The main result is a long exact sequence relating the homologies of these complexes for the whole group, the normal subgroup, and certain centralizer subgroups. The proof takes place at the level of partially-ordered sets. Notions of suspension and wedge product are considered in this context, which are analogous to the corresponding notions for topological spaces. We conclude with a formula for the generalized Steinberg module of a group with a normal subgroup, and give some examples.

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