• Korean Journal of Mathematics
• /
• v.7 no.1
• /
• pp.11-25
• /
• 1999

We will define a smooth fuzzy closure space and a subspace of it. We will investigate relationships between smooth fuzzy closure spaces and smooth fuzzy topological spaces. In particular, we will show that a subspace of a smooth fuzzy topological space can be obtained by the subspace of the smooth fuzzy closure space induced by it.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.31 no.2
• /
• pp.1-11
• /
• 2003

The purpose of this study is to investigate how five winning design proposals for the Seoul City Hall Plaza Design Competition have shown the spatial characteristics by comparing and reviewing them. Each design proposal shown different approaches that reveal the spatial characteristics. Through scrutinizing these design proposals, some similar and different aspects among them were identified. In order to examine these aspects, the winning design proposals were analysed and compared based on five categories such as design concepts, main facilities, representation of historical images, spatial connection, and event programs. Gilles Deleuze explained the spatial characteristics as striated space and smooth space. Striated space could be defined as sedentary space. It is distant vision-optical space that has dimensional, metric, and centered characteristics, whereas smooth space is defined as nomadic, close vision-haptic space that has directional and acentered characteristics. This study focused on the analysis of spatial characteristics according to smooth space and striated space. Based on the analysis of the spatial characteristics according to the smooth and striated space, some design proposals shown more characteristics of striated space while other proposals shown more characteristics of smooth space. Those design proposals that shown more characteristics of smooth space reveal flexible or changeable shape and void space, whereas the others that shown more characteristics of striated space try to suggest apparent guidelines for the future use by retaining the idea of a plaza through the concrete shape. This study, which analyzed the winning design proposals based on the spatial characteristics according to the smooth and striated space, can be used to analyze the designs and could help to develop a new methodology with a different perspective. furthermore, it could provide practical and creative design strategies for landscape design.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.23 no.1
• /
• pp.80-86
• /
• 2013

We give a new definition of ordinary smooth closure and ordinary smooth interior of an ordinary subset in an ordinary smooth topological space which have almost all the properties of the corresponding operators in a classical topological space. As a consequence of these definitions we reduce the additional hypotheses in the results of [1] and also generalize several properties of the types of compactness in [1].

• Journal of the Korean Institute of Intelligent Systems
• /
• v.22 no.6
• /
• pp.799-805
• /
• 2012

We introduce the notions of ordinary smooth, quasi-ordinary smooth and weak ordinary smooth structure, showing that various properties of an ordinary smooth topological space can be expressed in terms of these structures. In particular, the definitions and results of [2, 4, 5] may be expressed in terms of the ordinary smooth and quasi-ordinary smooth structures. Furthermore, we present the basic concepts relating to the weak ordinary smooth structure of an ordinary smooth topological space and the fundamental properties of the objects in these structures.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.12 no.1
• /
• pp.66-76
• /
• 2012

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.

• Korean Institute of Interior Design Journal
• /
• v.15 no.4 s.57
• /
• pp.156-164
• /
• 2006

One of frequent phenomena in the contemporary cultural field is the alternative or accompanying interweaving phenomena which happens in the relative connection of A, B, and C. The power of interweaving mixture is one of energies which unify the contemporary cultural phenomena, and it appears as a major phenomena in the recent popular digital architecture. In this study, the mixture, shape, and contents in the contemporary space design is analyzed as a point of view of Post-Structuralism. Namely, the digital part and non-digital part of alternative and circulating existence in the space are classified and the interweaving phenomena in the contemporary space design are proved. It is studied for digital part and physical space to conjunct the hole space and smooth space of Deleuze as part of interweaving phenomena. It is clear that the compatible concept of the hole space and smooth space is crossed complexly or is coexisting in circulating and extending, and is showed as interweaving phenomena in one space.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.8 no.3
• /
• pp.88-94
• /
• 1998

We will difine a base of a smooth fuzzy topological space and investigate some properties of bases. We will prove the existences of initial smooth fuzzy topological spaces. From this fact, we can define subspaces and products of smooth fuzzy topological spaces.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.539-541
• /
• 1997

Let X be a smooth projective threefold. Let C be a smooth projective curve and let $f : X \to C$ be a fiber space with connected fiber S. Assume that $q_1(S) = 0$. Then we have $-X(O_C)X(O_S) \leq -X(O_X)$.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.551-558
• /
• 2006

We establish a weak law of large numbers for sequence of random elements with values in p-uniformly smooth Banach space. Our result is more general and stronger than some well-known ones.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.30 no.2
• /
• pp.50-62
• /
• 2002

From modernism to post-modernism, the practice in the design field often reduced the complexity of environment and to remove variety. However, contemporary ideas of space have been changed. The current thought premise is that the environment is mutable and is evolving according to inner and outer forces and elements. Therefore, leading designers recognize that the environment is complex in itself while anticipating a new theory explaining on-going trends. The idea of fold formulated by Gilles Deleuze can provide a theoretical base for new environmental design in constrat to current design practices. The fold is a hybrid by accommodating complex relations within an object. It carries a dynamic world view through continual process and yields a topological space against absolute space like Euclid geometry. The characteristics of the fold can be paraphrased as rhizome, stratification and smooth space. Rhizome forms a non-hierarchial connection like networking in internet space. Stratification is a kind of superimposition of autonomous potential layers within a single object. Smooth space is a free space and event oriented space keeping non-linear form. This study tried to incorporate the idea of fold to environmental design methods and design process in order to make space which can correspond with complex environment and topological form. In the design process adapted to fold theory, rhizome analysis accepts the complexity of environment and stratification strategy embraces the possibility of accidental use. As a result, the designed park carries a monadic image and produces an ambiguous space. Lastly, smooth space makes topological space unlike Euclid geometry and is free space comosed by the user themselves. Transporting the idea of fold into environmental design could be an alterative way for indeterminate and flexible design to accept new identity of place. Therefore, this study accepts the concept of incidental morphogenesis to make space based on the complexity of environment. The designed space based on the idea of fold searches to create free event space determined by user rather than designated by designer.