• The Mathematical Education
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• v.16 no.2
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• pp.22-26
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• 1978

It is shown that a map having an extension to an open map between the Alex-androff base compactifications of its domain and range has a unique such extension. J.S. Wasileski has introduced the Alexandroff base compactifications of Hausdorff spaces endowed with Alexandroff bases. We introduce a definition of morphism between such spaces to obtain a category which we denote by ABC. We prove that the Alexandroff base compactification on objects can be extended to a functor on ABC and that the compact objects give an epireflective subcategory of ABC. For each topological space X there exists a completely regular space $\alpha$X and a surjective continuous function $\alpha$$_{x}$ : Xlongrightarrow$\alpha$X such that for each completely regular space Z and g$\in$C (X, Z) there exists a unique g$\in$C($\alpha$X, 2) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\alpha$$_{x}$, $\alpha$X) is called a completely regularization of X. Let TOP be the category of topological spaces and continuous functions and let CREG be the category of completely regular spaces and continuous functions. The functor $\alpha$ : TOPlongrightarrowCREG is a completely regular reflection functor. For each topological space X there exists a compact Hausdorff space $\beta$X and a dense continuous function $\beta$x : Xlongrightarrow$\beta$X such that for each compact Hausdorff space K and g$\in$C (X, K) there exists a uniqueg$\in$C($\beta$X, K) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\beta$$_{x}$, $\beta$X) is called a Stone-Cech compactification of X. Let COMPT$_2$ be the category of compact Hausdorff spaces and continuous functions. The functor $\beta$ : TOPlongrightarrowCOMPT$_2$ is a compact reflection functor. For each topological space X there exists a realcompact space (equation omitted) and a dense continuous function (equation omitted) such that for each realcompact space Z and g$\in$C(X, 2) there exists a unique g$\in$C (equation omitted) with g=g$^{\circ}$(equation omitted). Such a pair (equation omitted) is called a Hewitt's realcompactification of X. Let RCOM be the category of realcompact spaces and continuous functions. The functor (equation omitted) : TOPlongrightarrowRCOM is a realcompact refection functor. In [2], D. Harris established the existence of a category of spaces and maps on which the Wallman compactification is an epirefiective functor. H. L. Bentley and S. A. Naimpally [1] generalized the result of Harris concerning the functorial properties of the Wallman compactification of a T$_1$-space. J. S. Wasileski [5] constructed a new compactification called Alexandroff base compactification. In order to fix our notations and for the sake of convenience. we begin with recalling reflection and Alexandroff base compactification.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.86-89
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• 2003

To model a numerical problem space under the limitation of available data, we need to extract sparse but key points from the space and to efficiently approximate the space with them. This study proposes a sampling method based on the search process of genetic algorithm and a space modeling method based on least-squares approximation using the summation of Gaussian functions. We conducted simulations to evaluate them for several kinds of problem spaces: DeJong's, Schaffer's, and our original one. We then compared the performance between our sampling method and sampling at regular intervals and that between our modeling method and modeling using a polynomial. The results showed that the error between a problem space and its model was the smallest for the combination of our sampling and modeling methods for many problem spaces when the number of samples was considerably small.

• Journal of the Korean Society of Safety
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• v.24 no.6
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• pp.1-6
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• 2009

This study describes a construction procedure of 3D virtual space using the NGIS data and its application to simulation. 3D space topography is modeled by using DEM consisted with triangular regular network. The elevations of nodal points of DEM are calculated through the interpolation with contour line and elevation points from the NGIS. Also, data for 2D roads and their environments, such as trees, lamps, and traffic signals, were extracted from the NGIS and projected on the DEM surfaces to get 3D virtual space. To give a reality to 3D virtual space and accelerate its graphic speed, data were converted into the directX format. It is believed that the virtual space constructed in this work can be applicable to the ubiqutous because DEM data can be converted to the AutoCAD format and ASCII code.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.82.2-82.3
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• 2019

Korea Astronomy and Space Science Institute (KASI), in collaboration with the NASA Goddard Sparce Flight Center (GSFC), will develop a next generation coronagraph for the International Space Station (ISS). COronal Diagnostic EXperiment (CODEX) uses multiple filters to obtain simultaneous measurements of electron density, temperature, and velocity within a single instrument. CODEX's regular, systematic, comprehensive dataset will test theories of solar wind acceleration and source, as well as serve to validate and enable improvement of space-weather/operational models in the crucial source region of the solar wind. CODEX subsystems include the coronagraph, pointing system, command and data handling (C&DH) electronics, and power distribution unit. CODEX is integrated onto a standard interface which provides power and communication. All full resolution images are telemeters to the ground, where data from multiple images and sequences are co-added, spatially binned, and ratioed as needed for analysis.

• Journal of Gifted/Talented Education
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• v.21 no.4
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• pp.847-860
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• 2011

In this study, the instrument of mathematical thinking ability tests were considered, and the differences between gifted and regular high school students in the ability were investigated by the test. The instrument consists of 9 items, and verified its quality due to reliability. Participants were 353 regular and 252 gifted high school students from tenth grade. As a result, not only organizing ability of information but also ability of space perception and visualization and intuitive insight ability could be the characteristics of the mathematical giftedness.

• Bulletin of the Korean Space Science Society
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• 2010.04a
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• pp.36.2-36.2
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• 2010

Followed the System Design Review (PDR) of a mobile SLR (Satellite Laser Ranging) system, a successful preliminary design review was finished in 2009. With the completion of this mobile SLR system, KASI (Korea Astronomy and Space Science Institute) can perform a series of test observation and calibration/validation procedures. After the operation performance of the whole system reaches the nominal design, a regular scheduled observation will be executed. However, the project has been disturbed by the frequent change of working staff, budget profile, and plan as well as the inexperienced man power. In this study, the contents and the issues of PDR are briefly reviewed and several items of SLR system are suggested. This mobile SLR system will push Korea's Space Geodetic study further and will make us jump to another step to the Space Science in Korea.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.431-441
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• 2015

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. Our purpose of this study is to give new topologies on the family ${\tau}(X)$ of all topologies induced by old one and its ${\theta}$ topology and to compare them.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.463-473
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• 2009

Two $C^1$-mappings, whose domain is a connected compact $C^1$-Banach manifold modelled over a Banach space X over $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$ and whose range is a Banach space Y over $\mathbb{K}$, are introduced. Sufficient conditions are given to assert they share only a value. The proof of the result, which is based upon continuation methods, is constructive.

• The Mathematical Education
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• v.21 no.1
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• pp.19-21
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• 1982

In this paper, we define the z-S-closed spaces using the notions of zero-sets and S-closed spaces introduced by T. Thompson, and investigate some properties of these spaces. We also obtain the following results. If a space X is z-S-closed, then every cover of z-regular semiopen sets has a finite proximate subcover. A z-extremally disconnected z-QHC space is z-S-closed, z-S-closed is contagious.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.387-396
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• 2018

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a fixed topology on X and we will regard ${\tau}(X)$ a topological space. Our purpose of this study is to comparison new topologies on the family ${\tau}(X)$ of all topologies induced old one.