The continuum is here presented as a formal space by means of a finitary inductive definition. In this setting a constructive proof of the Heine-Borel covering theorem is given. 1 I n t r o d u c t i o n It is well known that the usual classical proofs of the Heine-Borel covering theorem are not acceptable from a constructive point of view (cf. [vS, F]). An intuitionistic alternative proof that...

In this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. In fact, we obtain someLowen-type  and Chang-type fuzzy topologies on general fuzzyautomata. To this end, first we define a Kuratowski fuzzy interioroperator which induces a  Lowen-type  fuzzy topology on the  set ofstates of a max- min general   fuzzy automaton. Also by  provingsome theorems, ...

Let L be the zero set of a nonconstant monic polynomial with complex coe¢ cients. In the context of constructive mathematics without countable choice, it may not be possible to construct an element of L. In this paper we introduce a notion of distance from a point to a subset, more general than the usual one, that allows us to measure distances to subsets like L. To verify the correctness of th...

1. Introduction The goal of this survey is to give an overview (from a topologist's prospective) of the theory of Kleinian groups in higher dimensions. The survey grew out of a series of lectures which I have given in the University of Maryland in Fall of 1991 and which I have decided to update and publish now, in the proceedings of the 3-rd Ahlfors-Bers Colloquium. This survey was greatly innu...

Recently, F.Smarandache generalized the Atanassov’s intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets. Also, this author de…ned the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology on an IFS and the neutrosophic topology. We show in this work that this is false.

Various authors have considered the Zero-rest-mass equation and the contour integral representation of its solutions. Ferber generalized these equations to supertwistor spaces with 2N odd components so that with N=O we get the standard ungraded twistors of Penrose. In this paper we use the Batchelor theorem toconstruct the natural super Twistor space with coarse topology with underlying sta...

An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable  spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalizati...

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of weight $D_s$, does not draw from curvature band but has a purely band-geometric origin. mean-field description, non-zero Chern number or fragile topology sets lower bound for which, via Berezinskii-Kosterlitz-Thouless mechanism, might explain relatively high superconducting trans...