Digital Lusternik–Schnirelmann category

Constructing personal digital library by multi-search and customized category

The current search tools for retrieving information on WWW are not suitable for building customized information repository because these search tools are designed for general users with the result of only an unstructured collection of documents. In this paper, we present a personal digital library capable of eficiently retrieving information on the World Wide Web. We adopt several new strategie...

Category of Polygroup Objects

Category of $H$-groups

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

On category of co-coverings

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

On the category of geometric spaces and the category of (geometric) hypergroups

‎In this paper first we define the morphism between geometric spaces in two different types‎. ‎We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎The relation between hypergroups and geometric spaces is studied‎. ‎By constructing the category $qh$ of $H_{v}$-groups we answer the question...