We prove non–existence of static, vacuum, appropriately regular, asymptotically flat black hole space–times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space–times, showing that the domains of outer communication of the Schwarzschild ...

We first derive a 3-dimensional impossible polycube by forcibly deforming the projection of a 3-dimensional polycube. This procedure is extended into n(≥4)-space to construct n-dimensional impossible polycubes represented in 2or 3-space. They are useful as fundamental grid patterns for imaging various n-dimensional impossible figures in our 3-space. On 2-space, especially, each pattern can be c...

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper an intuitionistic fuzzy regular weakly generalized closed set and intuitionistic fuzzy regular weakly generalized open set are introduced. Some of its properties are studied. Also we have provided some applications of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy rwT1/2 ...

Schwarz and Weck-Schwarz have shown that a T2-ordered space (X, τ, ) whose underlying topological space (X, τ) is completely regular need not be a completely regularly ordered space (that is, T3.5 + T2-ordered T3.5-ordered). We show that a completely regular T2-ordered space need not be completely regularly ordered even under more stringent assumptions such as convexity of the topology. One exa...

A cardinal λ is called ω-inaccessible if for all μ < λ we have μ < λ. We show that for every ω-inaccessible cardinal λ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density λ. This extends an analogous earlier result of ours that only worked for regular λ. In [1] we have shown that for any cardinal λ a natural CCC forcing...

We study the geometry of the leaf closure space of regular and singular Riemannian foliations. We give conditions which assure that this leaf space is a singular symplectic or Kähler space. In recent years physicists and mathematicians working on mathematical models of physical phenomena have realised that modelling based on geometric structures on now classical smooth manifolds is insufficient...

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point. In [Co] Cole gave a counterexample to the peak point conjecture by constructing a non-trivial uniform algebra A with co...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...