• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.813-828
• /
• 1999

In this paper, we give a Peleg type KKM theorem on G-convex spaces and using this, we obtain a coincidence theorem. First, these results are applied to a whole intersection property, a section property, and an analytic alternative for multimaps. Secondly, these are used to proved existence theorems of equilibrium points in qualitative games with preference correspondences and in n-person games with constraint and preference correspondences for non-paracompact wetting of commodity spaces.

• Journal of the Architectural Institute of Korea Planning & Design
• /
• v.34 no.3
• /
• pp.11-21
• /
• 2018

This paper explores the structure of space in architecture from a viewpoint that individual unitized spaces are gathered to form the whole. To understand the spatial structure of architecture, firstly we need to understand each unitized spaces, and secondly, one must understand how the following adjacent spaces are connected to form the whole building. this gives salience to a fact that understanding the whole comprehensively. It is the most fundamental bases that must be understood and unitized when understanding the spatial structure of an existing building and designing a new one. It is necessary to hypostatize space as an abstract notion. In regards to this space examines the logical flow of structure within actual space. Hypostasieren process includes the process of shaping space and the shape information. In this process we need to refer to the properties of space and the morphological characteristics of physical elements. The segment of the unitized space is the realization process of the basic space. This study aims to provide a theoretical basis for analysis and design of spatial structure by comparing several representative methods of segmenting unitized space.