A point p of a topological space X is a cut point of X if X − {p} is disconnected. Further, if X −{p} has precisely m components for some natural number m ≥ 2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y , we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is ...

An irreducible open 3-manifold W is R-irreducible if it contains no non-trivial planes, i.e. given any proper embedded plane Π in W some component of W −Π must have closure an embedded halfspace R × [0,∞). In this paper it is shown that if M is a connected, P-irreducible, open 3-manifold such that π1(M) is finitely generated and the universal covering space M̃ of M is R-irreducible, then either ...

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...

We study one-parameter curves on the universal Teichmüller space T and on the homogeneous space M = Diff S/Rot S embedded into T . As a result, we deduce evolution equations for conformal maps that admit quasiconformal extensions and, in particular, such that the associated quasidisks are bounded by smooth Jordan curves. Some applications to Hele-Shaw flows of viscous fluids are given.

In this paper,  we introduce  the notion of $M$-fuzzifying interval spaces, and discuss the relationship between $M$-fuzzifying interval spaces and $M$-fuzzifying convex structures.It is proved that  the category  {bf MYCSA2}  can be embedded in  the category  {bf  MYIS}  as a reflective subcategory, where  {bf MYCSA2} and   {bf  MYIS} denote  the category of $M$-fuzzifying convex structures of...

A knot k in a closed orientable 3-manifold is called nonsimple if the exterior of k possesses a properly embedded essential surface of nonnegative Euler characteristic. We show that if k is a nonsimple prime tunnel number one knot in a lens space M (where M does not contain any embedded Klein bottles), then k is a (1, 1) knot. Elements of the proof include handle addition and Dehn filling resul...

This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $...

Let $R$ be a commutative ring with identity and $M$ be a unitary$R$-module. The primary-like spectrum $Spec_L(M)$ is thecollection of all primary-like submodules $Q$ such that $M/Q$ is aprimeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ isa prime submodule for all $Qin Spec_L(M)$. This class containsthe family of multiplication modules properly. The purpose of thispaper is to intro...