Covering versus partitioning with Polish spaces

Covering Spaces

Continuous Ramsey Theory on Polish Spaces and Covering the Plane by Functions

We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number hm(c) of a pair-coloring c : [X]2 → 2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω , cmin and cmax, which satisfy hm...

Quasi-Polish Spaces

We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Π2 in the Borel hierarchy. ...

Packing, Partitioning, and Covering Symresacks

In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering (ppc) inequalities. To handle symmetries as well as ppc-constraints simultaneously, we introduce constrained symresacks which are the convex hull of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and which fulfill some ppc-constraint...

Noetherian Quasi-Polish spaces

In the presence of suitable power spaces, compactness ofX can be characterized as the singleton {∅} being open in the space A(X). Equivalently, this means that universal quantification over a compact space preserves open predicates. Using the language of represented spaces, one can make sense of notions such as a Σ 2 subset of the space of Σ 2 -subsets of a given space. This suggests higher-ord...