In this paper we formulate three problems concerning topological properties of sets generating Borel non-σ-compact groups. In case of the concrete Fσδ-subgroup of {0, 1}ω×ω this gives an equivalent reformulation of the Scheepers diagram problem.

Generalized Quasilinearization Method for Coincidences Adriana Buică and Radu Precup Faculty of Mathematics and Computer Science Babeş-Bolyai University 3400 Cluj, Romania [email protected], [email protected] Abstract An abstract unified theory of both monotone iterative and generalized quasilinearization methods is presented for operator equations of coincidence type in ordered Ban...

The purpose of this paper is to introduce and study a new generalization of ω-continuous multifunction called slightly ω-continuous multifunctions in topological spaces. AMS (MOS) Subject Classification Codes: 54C10, 54C08, 54C05

A Seifert matrix is a square integral matrix V satisfying det(V − V T ) = ±1. To such a matrix and unit complex number ω there is a signature, σω(V ) = sign((1 − ω)V + (1 − ω̄)V T ). Let S denote the set of unit complex numbers with positive imaginary part. We show {σω}ω∈S is linearly independent, viewed as a set of functions on the set of all Seifert matrices. If V is metabolic, then σω(V ) = 0...

A Seifert matrix is a square integral matrix V satisfying det(V − V T ) = ±1. To such a matrix and unit complex number ω there is a signature, σω(V ) = sign((1 − ω)V + (1 − ω̄)V T ). Let S denote the set of unit complex numbers with positive imaginary part. We show {σω}ω∈S is linearly independent, viewed as a set of functions on the set of all Seifert matrices. If V is metabolic, then σω(V ) = 0...

We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group G, and a 3-cocycle ω, which was first studied by Dijkgraaf, Pa...

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations of Sc(Onbd,O) and Smirnov-Sc(Onbd,O) in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which Sc(Onbd,O) is preserved by products. Among metrizable groups we characterize t...