Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringb...

There are two main approaches to obtaining “topological” cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed — for example, the category of sequential spaces. Under the other, one generalises the notion of space — for example, to Scott’s notion of equilogical space. In this paper we show that the two appr...

Based on the st~uctuzL~m, we propose a generative semantic model which has a topological information space generative grammar as basic rules. In this model a semantic map which is called a topological information space, is generated by the grammar,and the space can express implications and simi l a r i t i e s among concepts. In the syntax, a syntactic generative grammar is defined based on the...

Topological maps are graph-based representations of space and have been considered as an alternative to metric representations in the context of robot navigation. In this work, we seek to improve on the lack of robustness of current topological mapping systems against ambiguity in the available information about the environment. For this purpose, we develop a topological mapping system that tra...

A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in terms of simple cardinal invariants of the family of uniformly continuous pseudometrics of the given uniform space and of the uniformity itself....

We study damped hyperbolic equations on the infinite line. We show that on the global attracting set G the ε-entropy (per unit length) exists in the topology of W 1,∞. We also show that the topological entropy per unit length of G exists. These results are shown using two main techniques: Bounds in bounded domains in position space and for large momenta, and a novel submultiplicativity argument...

We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional gravity. The quantization of this theory in the unitary gauge can be consistently performed taking into account all the topological sectors arising from the gauge...

We introduce a natural generalization of Borel’s Conjecture. For each infinite cardinal number κ, let BCκ denote this generalization. Then BCא0 is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture,¬BCא1 is equivalent to the existence of a Kurepa tree of heightא1. Using the connection of BCκ with a generalization of Kurepa’s Hypothesis, we obtain the following...