Ultrafilter invariants in topological spaces

A notion of selective ultrafilter corresponding to topological Ramsey spaces

We introduce the relation of almost-reduction in an arbitrary topological Ramsey space R as a generalization of the relation of almostinclusion on N[∞]. This leads us to a type of ultrafilter U on the set of first approximations of the elements of R which corresponds to the well-known notion of selective ultrafilter on N. The relationship turns out to be rather exact in the sense that it permit...

METACOMPACTNESS IN L-TOPOLOGICAL SPACES

In this paper the concept of metacompactness in L-topologicalspaces is introduced by means of point finite families of L-fuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedL-topological spaces is also obtained.

Ultrafilter Spaces on the Semilattice of Partitions

The Stone-Čech compactification of the natural numbers βω (or equivalently, the space of ultrafilters on the subsets of ω) is a well-studied space with interesting properties. Replacing the subsets of ω by partitions of ω in the construction of the ultrafilter space gives non-homeomorphic spaces of partition ultrafilters corresponding to βω. We develop a general framework for spaces of this typ...

Topological Invariants for Lens Spaces and Exceptional Quantum Groups

A pressing problem in the field of ‘quantum topology’ [1][2] is to understand the topological information embodied in the quantum invariants of 3-manifolds[3] [5] constructed in recent years, and to use the information to settle geometric questions. A direct way to tackle the problem is to compute these invariants for 3-manifolds of interest, then try to extract topological information from the...

Ultrafilter Spaces on the Semilattice of Partitions