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Generated triangular norms

Erich Peter Klement, Radko Mesiar, Endre Pap (2000)

Kybernetika

An overview of generated triangular norms and their applications is presented. Several properties of generated t -norms are investigated by means of the corresponding generators, including convergence properties. Some applications are given. An exhaustive list of relevant references is included.

Generating methods for principal topologies on bounded lattices

Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2021)

Kybernetika

In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.

Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

For a locally symmetric space M , we define a compactification M M ( ) which we call the “geodesic compactification”. It is constructed by adding limit points in M ( ) to certain geodesics in M . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M ( ) for locally symmetric spaces. Moreover, M ( ) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

Hausdorff Fréchet closure spaces with maximum topological defect

Riccardo Ghiloni (2002)

Bollettino dell'Unione Matematica Italiana

It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number ω 1 . In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly ω 1 . Some classical and recent results are deduced from our criterion.

Hausdorffness in intuitionistic fuzzy topological spaces.

Francisco Gallego Lupiáñez (2003)

Mathware and Soft Computing

The basic concepts of the theory of intuitionistic fuzzy topological spaces have been defined by D. Çoker and co-workers. In this paper, we define new notions of Hausdorffness in the intuitionistic fuzzy sense, and obtain some new properties, in particular on convergence.

HC-convergence theory of L -nets and L -ideals and some of its applications

A. A. Nouh (2003)

Mathematica Bohemica

In this paper we introduce and study the concepts of error -closed set and error -limit ( error -cluster) points of L -nets and L -ideals using the notion of almost N -compact remoted neighbourhoods in L -topological spaces. Then we introduce and study the concept of error -continuous mappings. Several characterizations based on error -closed sets and the error -convergence theory of L -nets and L -ideals are presented for error -continuous mappings.

H-closed extensions with countable remainder

Daniel K. McNeill (2012)

Commentationes Mathematicae Universitatis Carolinae

This paper investigates necessary and sufficient conditions for a space to have an H-closed extension with countable remainder. For countable spaces we are able to give two characterizations of those spaces admitting an H-closed extension with countable remainder. The general case is more difficult, however, we arrive at a necessary condition — a generalization of Čech completeness, and several sufficient conditions for a space to have an H-closed extension with countable remainder. In particular,...

Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Boaz Tsaban, Lubomyr Zdomsky (2012)

Journal of the European Mathematical Society

A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii α 1 spaces, for which every sheaf at a point can be amalgamated in a natural way. Let C p ( X ) denote the space of continuous real-valued functions on X with the topology of pointwise convergence. Our main result...

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