Uniform Harnack inequalities for harmonic functions on the preand graphical Sierpinski carpets are proved using a probabilistic coupling argument. Various results follow from this, including the construction of Brownian motion on Sierpinski carpets embedded in Md , d > 3, estimates on the fundamental solution of the heat equation, and Sobolev and Poincaré inequalities. The Sierpinski carpets (S...

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.

In this paper, we consider a large variety of solutions for the generation of Sierpinski triangles, one of the case studies for the AGTIVE graph transformation tool contest [15]. A Sierpinski triangle shows a well-known fractal structure. This case study is mostly a performance benchmark, involving the construction of all triangles up to a certain number of iterations. Both time and space perfo...

In this paper, the concepts of pairwise fuzzy Baire bitopological spaces are introduced and characterizations of pairwise fuzzy Baire bitopological spaces are studied. Several examples are given to illustrate the concepts introduced in this paper.

We study structures called d-frames which were developed by the last two authors for a bitopological treatment of Stone duality. These structures consist of a pair of frames thought of as the opens of two topologies, together with two relations which serve as abstractions of disjointness and covering of the space. With these relations, the topological separation axioms regularity and normality ...

The aim of this paper is to introduce the concept of Λ operator of a fuzzy set in a fuzzy bitopological space.Then we study (i, j)-fuzzy Λγ -set and its properties. Moreover, we define (i, j)-fuzzy Λ-closed set, (i, j)-fuzzy Λγ -closed set and (i, j)-fuzzy generalized closed set in fuzzy bitopological space. The concepts of (i, j)-fuzzy Λ-closed set and (i, j)-fuzzy generalized closed set are i...

It is well known [Hoc69, Joy71] that profinite T0-spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (1) (X,τ) is a profinite topological space. (2) The T0-reflection of (X,τ) is a profinite T0-space. (3) (X,τ) is a quasi spectral space (in the sense of [BMM08]). (4) (X,τ) admits a ...

We modify the concept of θ-regularity for spaces with 2 and 3 topologies. The new, more general property is fully preserved by sums and products. Using some bitopological reductions of this property, Michael’s theorem for several variants of bitopological paracompactness is proved.

In this paper, we built bitopological space on the concept of neutrosophic soft set, defined basic topological concepts spaces which are N3-(bi)*-open N3-(bi)*-closed (bi)*-neutrosophic interior, (bi)* closure, boundary, exterior and introduced their properties. addition, investigated relations these with counterparts in many examples.