• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.105-113
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• 1994

In the course of study of dendroids, Czuba [3] introduced a notion of $R^{i}$ -continua which is a generalization of R-arc [1]. He showed a new class of non-contractible dendroids, namely of dendroids which contain an $R^{i}$ -continuum. Subsecequently Charatonik [2] attempted to extend the notion into hyperspace C(X) of metric continuum X. In so doing, there were some oversights in extending some of the results relating $R^{i}$ -continua of dendroids for metric continua. In fact, Proposition 1 in [2] is false (see example C below) and his proof of Theorem 6 in [2] is not correct (Take Example 4 in [4] with K = [e,e'] as an $R^{1}$-continuum of X and work it out. Then one seens that K not .mem. K as he claimed otherwise.). The aims of this paper are to introduce a notion of w-regular convergence which is weaker than 0-regular convergence and to prove that the w-regular convergence of a sequence {Xn}$^{\infty}$$_{n=1}$ to $X_{0}$ of subcontinua of a metric continuum X is a necessary and sufficient for the sequence {C( $X_{n}$)}$^{\infty}$$_{n=1}$ to converge to C( $X_{0}$ ), and also to prove that if a metric continuum X contains an $R^{i}$ -continuum with w-regular convergence, then the hyperspace C(X) of X contains $R^{i}$ -continuum.inuum.uum.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.151-155
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• 2016

In this paper, we show that if a continuum-wise expansive homeomorphism on a compact connected metric space is shadowing then it is topologically stable. This generalizes the main result of [4].

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.647-651
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• 2015

Let (X, d) be a compact metric space, and let $f:X{\rightarrow}X$ be a continuous map. We consider that if a positively continuum-wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.

• Kyungpook Mathematical Journal
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• v.10 no.1
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• pp.65-68
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• 1970

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.309-319
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• 1997

We introduce $R^i$-sets and give various relations between $R^i$-sets and prove that the hyperspace of a metric continuum containing any one of the $R^i$-set also contains $R^i$ and hence is not contractible.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.225-231
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• 1997

In 1970's Goodykoontz gave characterizations of connectedness imkleinen and locally arcwise connectedness of $2^X$ only at singleton set {x} ${\epsilon} 2^X$ [5,6,7]. In [7], we gave necessary conditions for C(X) to be arcwise connected im kileinen at any point $A {\epsilon} C(X)$.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1421-1431
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• 2021

In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C⁰-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

• Tunnel and Underground Space
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• v.24 no.4
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• pp.255-274
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• 2014

The target of this study is large scale rock slope collapsed by around 7 pm on August, 2012, which is located at ${\bigcirc}{\bigcirc}$ limestone quarries of Gangneung city, Gangwondo. The slope prior to the collapse is formed as the height of about 200 m and the average inclination of $45^{\circ}$. The estimated amount of the collapse is about $1,500,000m^3$ with respect to the slope after the collapse. Geotechnical and field investigations such as boring, geophysical prospecting, surface geological survey, geological lineaments, borehole imaging, metric 3D imaging, experimental and field test, mining work by year, and daily rainfall were performed to find the cause of rock slope failure. Various analyzes using slope mass rating, stereonet projection, limit equilibrium method, continuum and non-continuum model were conducted to check of the stability of the slope. It is expected that the cause of slope failure from the results of various analysis and survey is due to the combined factors such as topography, rainfall, rock type and quality, discontinuities, geo-structural characteristics as the limestone cavity and fault zones, but the failure of slope in case of the analysis without the limestone cavity is not occurred. Safe factor of 0.66 was obtained from continuum analysis of the slope considering the limestone cavity, so the ultimate causes of slope failure is considered to be due to the influence of limestone cavity developed along fault zone.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• v.2 no.1
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• pp.53-61
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• 2021

Distribution of fish community depends largely on environmental disturbance such as habitat change. In this study, we evaluated the impact of environmental variables and microhabitat patch types on fish distribution in Yudeung Stream at 15 sites between early May and late June 2019. We used non-metric multidimensional scaling to examine the distribution patterns of fish in each site. Gnathopogon strigatus, Squalidus gracilis majimae, Zacco koreanus, and Zacco platypus were associated with riffle and boulder areas, whereas Iksookimia koreensis, Acheilognathus koreensis, Coreoleuciscus splendidus, Sarcocheilichthys nigripinnis morii, and Odontobutis interrupta were associated with large shallow areas. In contrast, Cyprinus carpio, Carassius auratus, Lepomis macrochirus, and Micropterus salmoides were found at downstream sites associated with large pool areas, sandy/clay-bottomed areas, and vegetated areas. On the basis of these results, we suggest that microhabitat patch types are important in determining the diversity and abundance of fish communities, since a mosaic of different microhabitats supports diverse fish species. As such, microhabitat patches are key components of freshwater stream ecosystem heterogeneity, and a suitable patch composition in stream construction or restoration schemes will support ecologically healthy food webs.

• Korean Journal of Ecology and Environment
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• v.55 no.2
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• pp.132-144
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• 2022

The fish community in the Seomjin River-Seomjin River Estuary-Gwangyang Bay coast continuum was investigated three times from March 2019 to October 2019. The collected species at the eight sites during the survey period were 49 species belonging to 31 families, including two endangered species. According to Bray-Curtis similarities, observations were divided into four groups based on the fish community composition; two groups (group 1, 2) and two uncategorized groups (group 3, 4). ANOSIM based on spatial and temporal groupings indicated that the spatial differences in fish communities (R=0.398, P=0.001) were relatively more important than the temporal differences (analysis of similarities, R=0.273, P=0.002). In particular, there were significant differences between groups 1 and 2 (analysis of similarities, R=0.556, P=0.001), and similarity percentage analysis revealed that Argyrosomus argentatus (9.4%), Favonigobius gymnauchen (6.9%) and Konosirus punctatus (5.9%) contributed to these differences of fish assemblages for each group. The fish fauna distributed in the Seomjin River-Gwangyang Bay ecosystem were spatially divided and the number of species and number of individuals showed seasonal differences. This study could be a basis for understanding changes in the fish community and implementing conservation and management strategies on major species within a continuous environment of the river-estuary-ocean continuum.