• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

• Journal of the Korean Institute of Educational Facilities
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• v.24 no.1
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• pp.3-10
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• 2017

This study is to analyze the remodeling method of library in terms of space extension method and urban regeneration by repurposing function in unused facilities through case study. In many case of library extension, horizontal extensions are more frequent than vertical extensions, because there are limits to extend vertically due to high live load estimation by book stacks. Extension schemes was organized by new building extension method in connection with existing buildings, attaching method small scaled mass or linear mass to existing building, connecting method a plurality of existing small buildings, vertical extension method on the top of the structure, underground extension method using special structure. Unused facility remodeling to the library, large scaled buildings can be developed completely to the function of the library through the relocation of the space, while small scaled building needs spatial extension. In the case of spatial extension, existing space that was used for other purposes can be used as a reading room or office, avoiding high live load estimation.

• The Mathematical Education
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• v.22 no.3
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• pp.27-31
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• 1984

In this paper we summarize the characteristic properties of the nuclear space, and then try to establish the relation between Hopf's extension theorem and nuclear space on $\sigma$-Hilbert space.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.461-475
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• 2024

The concept of an extension α-F-contraction and it's modified counterpart represents an advancement in the theory of metric space contractions. Through our study of the contraction principles and it's relationship to extension and modified extension, we found different conditions somewhat lengthy. In our paper, we create a development of the conditions for the extension of α-F-contraction and a modified α-F-contraction by reducing the conditions and make them easier. Our propose conditions are notably simple and effective. They serve as the foundation for proving theorems and solving examples that belong to our study. Moreover, they have remarkable significance in the condition of mathematical analysis and problem-solving. Thus, we find that these new conditions that we mention in the definitions achieve what is require and through them, we choose λ = 1 and we choose λ ∈ (0, 1) to clarify our ideas.

• Korean Institute of Interior Design Journal
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• v.21 no.2
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• pp.152-162
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• 2012

In Korean apartment housing, balcony is semi-outdoor space for storage and drying laundry. Recently, this semi-outdoor balcony space has been merged into indoor living space with the legal permission of balcony extension. It results in disappearance of the original function of balcony in apartment housing. This study attempts to propose better utilization of balcony extension by analyzing how balcony has been extended and used, and what residents' needs are. This study asks 400 housewives living in apartment housing in Jangyu new urban area, Kyungnam. Findings are : 1) Balcony extensions are carried out in a living room, a large bedroom and a small bedroom. Most extensions are made for enlarging adjacent indoor living space; 2) Original balcony that is not extended is used for drying laundry, resting, flower pot, storing, and kid's playing; 3) The residents recognize that problems of balcony extension are the decreased heating efficiency, the reduced soundproofing effect, the loss of spare housework space, and the disappearance of buffer between indoor and outdoor space; 4) Many residents want to extend their balcony space of a small bedroom and a large bedroom and to keep the balcony space of a kitchen-dining room and a master bedroom as they are.

• Journal of the Korean housing association
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• v.15 no.1
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• pp.215-222
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• 2004

• Korean Institute of Interior Design Journal
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• v.23 no.1
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• pp.52-60
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• 2014

The purpose of this study is to analyze about the extension of user experience in the digital space. Through the digital technology and virtual space, the city's new environment is being changed. it makes people activate their aesthetic experience. Simultaneously, it elevates satisfaction levels regarding people's aesthetic experience. Research methods and settings of the range to study on the Extension of User Experience are as follows: First, establish digital space's characteristics comparing digital space at the structural change-points in modern society. Second, experience's approch way through the digital media in the contemporary space. And understand the concept about a variety of User Experience. Third. to classify the elements of access control for the user experience. Experience is being expanded through the generation process. Fourth, investigate analysis of the case studies, focused on the architecture and space design_Media installations that appear in the city park, the city's landmark buildings facade, the building facade by offering commercially applied for brand marketing_ announced through the media recently. Also, it is to look at the physical elements through digital media and to analyze the applicability of the public space. Therefore, the new approach to digital implementation shall be determined by looking in the direction of the user approaches.

• Korean Institute of Interior Design Journal
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• v.17 no.3
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• pp.148-155
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• 2008

The following research focuses on the formation method of digital space by organistic line extension among various digital formation methods. The paper reflects on the meaning and concept of today's digitalism which enables the application of complex organistic system on space through advanced technology. It also explores the concept of a line in topology which differs in assumptive meaning from traditional Euclidian geometry. The findings of the research are that first, digital space is not optimized, but is a tentative formation in process. A digital space encompasses characteristics such as infinity, possibility, potential, asymmetry, and the force of virtuality such characteristics are expressed through a moving surface constantly changing with direction. Second, a digital space formed by line extension is inseparable and durable since no measurement or dimension is predetermined. Furthermore, its sense of direction and flexibility gives it a feeling of a living organism. Third, a Euclidian methodology called 'NURBS' is being developed to express such a dynamic digital space; this is reflected through three elements, control point, weights, and knots to effectively reflect the characteristics of virtuality. The opportunities of digital space are infinite, and the possibilities of formation methods likewise vast.

• Journal of architectural history
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• v.23 no.6
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• pp.7-20
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• 2014

The purpose of this paper is to study on the architecture and extension project for the Church of St. Lorenzo. This study is composed of a through analysis of the extension elements on the church building and extension type for extension project of the Church of St. Lorenzo. The results of study are as follows: 1. The extension project for the Church of St. Lorenzo was basically consisted of the concept of a horizontal extension plan through both the interior and exterior space of the church building. This project was the plan of concept of additional or affixing extension through existing spaces with necessary spaces to make up for the previous simple space and form as well as functional aspect. 2. The unit spaces of the nave, the aisle, the small chapels bilaterally adorning the aisles, the transept and the chapels around transepts, and the sacristies by the extension project for the Church of St. Lorenzo is composed of regulation, balance and harmony as geometric space composition according to simple proportion system on whole and parts as well as parts and parts, through the definite articulation by each space zoning. 3. The most important innovative aspect different to previous churches in the extension project for the Church of St. Lorenzo is the compositive system of each other symmetrical spaces through long centrical axis of central part, applying the module system for horizontal arrangement. In particular, the use of regular module on repetition and proportion of rhythm from architectural composition system was precisely composed with the alter that consists of visual focus to express more accurate perspective.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.691-702
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• 1994

Let X be a normed linear space, M a subspace of X, and V a subspace of the dual space $X^*$. In [3], we studied the Hahn-Banach extension property in V. Here we give the definition and a characterization of the Hahn-Banach extension property in V.