Nearly prime subsemigroups of ßN.
Neighborhood base at the identity of free paratopological groups
In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.
Neighborhoods of the identity of the free abelian topological groups
Network character and tightness of the compact-open topology
For Tychonoff and an infinite cardinal, let the minimum number of cozero-sets of the Čech-Stone compactification which intersect to (generalizing -defect), and let . Give the compact-open topology. It is shown that , where: is tightness; is the network character; is the Lindel"of number. For example, it follows that, for Čech-complete, . The (apparently new) cardinal functions and are compared with several others.
New closure conditions and some problems in loop theory.
No semi topological monoid can be defined on the closure of the set { (x,sin 1 x) : xeR {o...
Non-abelian group structure on the Urysohn universal space
We prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We list several related open problems.
Noncompact semigroup actions.
Non-Hausdorff groupoids, proper actions and -theory.
Nonmetrizable topological dynamical characterization of central sets
Without the restriction of metrizability, topological dynamical systems are defined and uniform recurrence and proximality are studied. Some well known results are generalized and some new results are obtained. In particular, a topological dynamical characterization of central sets in an arbitrary semigroup (G,+) is given and shown to be equivalent to the usual algebraic characterization.
Nonreversibility of subsemigroups of semi-simple Lie groups.
Normed versus topological groups: Dichotomy and duality [Book]
Normen auf freien topologischen Gruppen.
Note on a generalization of a theorem of Bogolioùboff
Note on a Paper of T. Lezanski Concerning ΄΄Almost Reciprocal Operations΄΄
Note on analytic Moufang loops
It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.
Notes on compact semigroups with identity.
Numerical isotonies of preordered semigroups through the concept of a scale.