• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.175-182
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• 2008

This paper is a revised version of [5]. In [5], we define' nearness between two points' in a topological space in many ways and show that a continuous function preserves one-sided nearness. We also show that a $T_1$-space is characterized by one-sided nearness exactly. In this paper, we introduce extremally disconnected spaces and show that the new topology generated by the set of equivalence classes as a base is extremally disconnected.

• East Asian mathematical journal
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• v.35 no.2
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• pp.239-257
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• 2019

The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.

• Journal of Korean Academy of Nursing
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• v.25 no.3
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• pp.510-537
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• 1995

Human health is an integral part of experience in the process of Human Becoming. Through continual interaction with the environment human beings freely choose experience and develop as responsible beings. The process of the health experience of patient with terminal cancer is a unique. he objective of this study is to understand the lived experience of patients with terminal cancer in order to provide basic information for nursing care in the clinical setting and to develop a theoretical background for clinical practice. This study is to de-scribe and define the lived experience of patients with terminal cancer in order to provide a foundation for nursing research and education. Data collection has been done between December 1993 and November 1994. The subjects included five persons -four females and one male : one who was in her sixties, one in his fifties, two in their forties, and one who was in her thirties. The researcher has met with these patients 35 times, but at eight times the patient was in a stuporous condition and not able to participate, so these were not included in the data analysis. Parse's "Human Becoming Methodology", an existential phenomenological research methodology is used for this study. Data has been collected using he dialogical engagement process of "I and You", the participant researcher and the participant subject. Dialogical engagement was discontinued when the data was theoretically saturated. Data was analyzed using the extraction - synthesis and heuristic interpretation. The criteria of Guba and Lincoln(1985). and Sandelo wski(1986) : credibility, auditability, fitness and objectivity were used to test the validity and reliability of the data. The following is a description of the structure of the lived experience of patients with terminal cancer as defined by this study : 1. Structure : 1) Suffering through the reminiscence of past experience 2) The appearance of complex emotions related to life and connectedness 3) The increasing importance of significant people and of the Absolute Being 4) The increasing realization of the importance of health and belief 5) Desire for a return to health and a peaceful life or for acceptance of dying and a comfortable death In summary the structure of the lived experience of these patients can be said to be : suffering comes through reminiscence of past experience, and there are complex emotions related to life and connectedness. Significant people and the Absolute Being become increasingly important along with a realization of the importance of health and faith. And finally there is a desire for either a return to health and a peaceful life or for the acceptance of dying and a comfortable death. 2. Heuristic Interpretation : Using Parse's Human Becoming Methodology, the structure of the lived experience of patients with terminal cancer identified in this research is interpreted as. The lived experience of patients with terminal cancer involves the solving of past conflicts, and the experience of the healing and valuing of sorrow and pain. Through the relation of life and health, and the complex emotions that arise, the lived experience of revealing - concealing is of paradoxical emotions. The increasing importance of significant others and of the Absolute Being shows Connecting and Separating an on- going process of nearness and farness. Revision of thoughts about health and faith is interpreted as transforming and desire for restoration to health and a peaceful life or acceptance of dying and a cowfortable death, as powering. In summary, it is possible to see, in the lived experience of patients with terminal cancer, the relationship of the five concepts of Parse's theory : valuing, revealing -concealing, connecting-separating, transforming, and powering. From Parse's theory, the results of this study show that meaning is related to valuing, rhythmicity to revealing-concealing and connect-ing-separating, and cotranscendence to transforming and powering.