Search

In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed.

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic group $G$. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also give the cover of crossed modules within topological groups with operations., Comment: 15 pages, research paper, LaTeX2e, xypic

Golchin and Rezaei (Commun Algebra 2009; 37: 1995--2007) introduced the weak version of Condition $(PWP)$ for $S$-posets, called Condition $(PWP)_{w}$. In this paper, we continue to study this condition. We first present a necessary and sufficient condition under which the $S$-poset $A(I)$ satisfies Condition $(PWP)_{w}$. Furthermore, we characterize pomonoids $S$ over which all cyclic (Rees factor) $S$-posets satisfy Condition $(PWP)_{w}$, and pomonoids $S$ over which all Rees factor $S$-posets satisfying Condition $(PWP)_{w}$ have a certain property. Finally, we consider direct products of $S$-posets satisfying Condition $(PWP)_{w}$.

In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant submanifold to be a hemi-slant product. We also study these types of submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds.

We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first order theory of non abelian free groups, $T_{fg}$, is $n$-ample for any $n\in\omega$. This result adds to the work of Pillay, that proved that $T_{fg}$ is non CM -trivial. The sequence witnessing ampleness is a sequence of primitive elements in $F_{\omega}$. Our result provides an alternative proof to the main result of a preprint by Ould Houcine-Tent. We also add an appendix in which we make a few remarks on Sela's paper on imaginaries in torsion free hyperbolic groups. In particular we give alternative transparent proofs concerning the non-elimination of certain imaginaries., Comment: 22 pages, 2 figures. To appear in the Turkish Journal of Mathematics. Replaces arXiv:1205.4662

Recall that a map T \colon C(X,E) \to C(Y,F), where X, Y are Tychonoff spaces and E, F are normed spaces, is said to be separating, if for any 2 functions f,g \in C(X,E) we have c(T(f)) \cap c(T(g))= \varnothing provided c(f) \cap c(g) = \varnothing. Here c(f) is the co-zero set of f. A typical result generalizing the Banach--Stone theorem is of the following type (established by Araujo): if T is bijective and additive such that both T and T-1 are separating, then the realcompactification n X of X is homeomorphic to n Y. In this paper we show that a similar result is true if additivity is replaced by subadditivity (a map T is called subadditive if ||T(f+g)(y)|| \leq ||T(f)(y)||+ ||T(g)(y)|| for any f,g \in C(X,E) and any y \in Y). Here is our main result (a stronger version is actually established): if T \colon C(X,E) \to C(Y,F) is a separating subadditive map, then there exists a continuous map SY\colon b Y \rightarrow b X. Moreover, SY is surjective provided T(f)=0 iff f=0. In particular, when T is a bijection such that both T and T-1 are separating and subadditive, b X is homeomorphic to b Y. We also provide an example of a biseparating subadditive map from C(R) onto C(R), which is not additive.

In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.

In this paper, we introduce and study V -Gorenstein at modules and show the stability of the category of V -Gorenstein at modules. We investigate the existence of V -Gorenstein at covers and V -Gorenstein at preenvelopes for any left R -module. Also we prove that ( V - GF ;V - GF ? ) is a perfect hereditary cotorsion pair in B l ( R) , where V - GF stands the class of V -Gorenstein at left R -modules and B l ( R) is the left Bass class. Some applications are given.

In this paper, we introduce and study Ext-strongly Gorenstein projective modules. We prove that the class of Ext-strongly Gorenstein projective modules is projective resolving. Moreover, we consider Ext-strongly Gorenstein projective precovers.

General rotational surfaces as a source of examples of surfaces in the 4-dimensional Euclidean space were introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the basis of our invariant theory of spacelike surfaces we study general rotational surfaces with special invariants. We describe analytically the flat general rotational surfaces and the general rotational surfaces with flat normal connection. We classify completely the minimal general rotational surfaces and the general rotational surfaces consisting of parabolic points.