Abstract. When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to all of them belong to this class. The collections with the formulated property are said to be strongly join permitting for the given class (the no...

Joining independent quantum searches provides novel collective modes of quantum search (merging) by utilizing the algorithm’s underlying algebraic structure. If n quantum searches, each targeting a single item, join the domains of their classical oracle functions and sum their Hilbert spaces (merging), instead of acting independently (concatenation), then they achieve a reduction of the search ...

A fake lens space is an orbit space of a free action of a finite cyclic group on a sphere and as such it is a generalization of a classical lens space. The invariants of fake lens spaces described here are their homotopy groups, homology groups, a certain k-invariant, the Reidemeister torsion, the ρ-invariant and certain splitting invariants. We survey the classification of fake lens spaces whi...

Let A be a topological space which is not finitely generated and CH(A) denote the coreflective hull of A in Top. We construct a generator of the coreflective subcategory SCH(A) consisting of all subspaces of spaces from CH(A) which is a prime space and has the same cardinality as A. We also show that if A and B are coreflective subcategories of Top such that the hereditary coreflective kernel o...

A fake lens space is an orbit space of a free action of a finite cyclic group on a sphere and as such it is a generalization of a classical lens space. The invariants of fake lens spaces described here are their homotopy groups, homology groups, a certain k-invariant, the Reidemeister torsion, the ρ-invariant and certain splitting invariants. We survey the classification of fake lens spaces whi...