A subset of vertices in a graph is called total dominating set if every vertex the adjacent to at least one this set. minimal it does not properly contain another In paper, we study graphs whose all sets have same size, referred as well-totally-dominated (WTD) graphs. We first show that WTD with bounded domination number can be recognized polynomial time. Then focus on two. case, characterize t...

Comfort, W.W. and J. van Mill, Some topological groups with, and some without, proper dense subgroups, Topology and its Applications 41 (1991) 3-15. Continuing earlier investigations into the question cf the existence of a proper dense subgroup of a given topological group, the authors obtain some positive and some negative results, as follows: (a) Every non-degenerate connected Abelian group c...

The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the fam...

We characterize the Hurewicz covering property in metrizable spaces in terms of properties of the metrics of the space Theorem 1. Then we show that a weak version of selective screenability, when combined with the Hurewicz property, implies selective screenability Theorem 4. 1. Definitions and notation Let X be topological space. We shall use the notation O to denote the collection of all open ...

A lattice-ordered group (/-group) is said to be regular il no positive element of the group is disjoint from any of its conjugates. It is well known that every simple regular /-group is totally ordered [S]. The subgroups of the reals are the most elementary examples of regular simple /-groups; other examples can be found in [2] and [ó]. In this note we investigate a class of simple /-groups at ...

For any hyperbolic 3-manifold M with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of ∂M or the volume of M is bounded above. When the volume is bounded above, then area of ∂M is bounded above and the length of closed geodesic on ∂M is bounded below...

In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups  including, n$-$Bourbaki-bounded homomorphisms and$hspace{1mm}$ B$-$Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous homomorphisms. So, two topologies are presented on them a...

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...