Segal's multisimplicial spaces

Some sufficient conditions on a simplicial space $X$ guaranteeing that $X_1\simeq \Omega|X|$ were given by Segal. We give a generalization of this result for multisimplicial spaces. This generalization is appropriate for the reduced bar construction, providing an $n$-fold delooping of the classifying space of a category.Comment: 12 page

Coherence for Modalities

Positive modalities in systems in the vicinity of S4 and S5 are investigated in terms of categorial proof theory. Coherence and maximality results are demonstrated, and connections with mixed distributive laws and Frobenius algebras are exhibited.Comment: 43 pages, minor addition

Constraints and possibilities of the rural tourism development with the special stress on the case of Croatia

Global economic restructuring has created a climate in which many local economies have to adjust in order to maintain or enhance their socio-economic viability. Social and economic forces operating at the global level are determining both the nature and form of the rural landscape and how we value and use it. These changes, coupled with new ideas and approaches to leisure and recreation time are encouraging tourism development in rural areas at an ever increasing pace. The definition of rural tourism has been subject of much debate in the literature without arriving at any firm consensus. Most definitions tend to focus on the types of activities visitors engage with in a rural area, this leads to labelling of different tourism types. For example, forms associated with rural areas are agri tourism, eco tourism, green tourism, cultural tourism, heritage tourism, nature tourism and countryside tourism. All of these forms are closely associated with the basic requirements of sustainable development. What mustn't be overlooked as the very essence of rural tourism is local cooperation and community involvement through different forms of networking. This is supposed to be one of the most important requirements for rural tourism to become sustainable in the long term. The main objective of this paper is to examine the trends of rural tourism development in Europe and to highlight most obvious constraints to its better development in the context of sustainability. In this context some suggestions will be given so as to enhance future development of the rural tourist destinations in general and especially in the Republic of Croatia where this form of tourism is still underdeveloped. Key words: rural tourism destinations, sustainable development, networking, Croatia