• Title/Summary/Keyword: sequentially closed

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ON SPACES IN WHICH COMPACT-LIKE SETS ARE CLOSED, AND RELATED SPACES

  • Hong, Woo-Chorl
    • Communications of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.297-303
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    • 2007
  • In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is $Fr\acute{e}chet$-Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits ${\equiv}KC{\equiv}C-closed{\equiv}SC-closed$, and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.

THE κ-QUOTIENT IMAGES OF METRIC SPACES

  • Lin, Shou;Zheng, Chunyan
    • Communications of the Korean Mathematical Society
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    • v.27 no.2
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    • pp.377-384
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    • 2012
  • In this paper some properties of sequentially closed sets and $k$-closed sets in a topological space are discussed, it is shown that a space is a $k$-quotient image of a metric space if and only if its each sequentially closed set is $k$-closed, and some related examples about connectedness are obtained.

A NOTE ON SPACES WHICH HAVE COUNTABLE TIGHTNESS

  • Hong, Woo-Chorl
    • Communications of the Korean Mathematical Society
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    • v.26 no.2
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    • pp.297-304
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    • 2011
  • In this paper, we introduce closure operators [${\cdot}$]c and [${\cdot}$]a on a space and study some relations among [${\cdot}$]c, [${\cdot}$]a and countable tightness. We introduce the concepts of a strongly sequentially closed set and a strongly sequentially open set and show that a space X has countable tightness if and only if every strongly sequentially closed set is closed if and only if every strongly sequentially open set is open. Finally we find a generalization of the weak Fr$\'{e}$chet-Urysohn property which is equivalent to countable tightness.

ON SEQUENTIALLY g-CONNECTED COMPONENTS AND SEQUENTIALLY LOCALLY g-CONNECTEDNESS

  • Vijayashanthi, Palanichamy
    • Korean Journal of Mathematics
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    • v.29 no.2
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    • pp.355-360
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    • 2021
  • In this paper, we introduce the definition of sequentially g-connected components and sequentially locally g-connected by using sequentially g-closed sets. Moreover, we investigate some characterization of sequentially g-connected components and sequentially locally g-connected.

ON SEQUENTIAL TOPOLOGICAL GROUPS

  • Ince, Ibrahim;Ersoy, Soley
    • The Pure and Applied Mathematics
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    • v.25 no.4
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    • pp.243-252
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    • 2018
  • In this paper, we study the sequentially open and closed subsets of sequential topological groups determined by sequentially continuous group homomorphism. In particular, we investigate the sequentially openness (closedness) and sequentially compactness of subsets of sequential topological groups by the aid of sequentially continuity, sequentially interior or closure operators. Moreover, we explore subgroup and sequential quotient group of a sequential topological group.

ON SPACES WHICH HAVE COUNTABLE TIGHTNESS AND RELATED SPACES

  • Hong, Woo-Chorl
    • Honam Mathematical Journal
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    • v.34 no.2
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    • pp.199-208
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    • 2012
  • In this paper, we study some properties of spaces having countable tightness and spaces having weakly countable tightness. We obtain some necessary and sufficient conditions for a space to have countable tightness. And we introduce a new concept of weakly countable tightness which is a generalization of countable tightness and show some properties of spaces having weakly countable tightness.

SOME NECESSARY AND SUFFICIENT CONDITIONS FOR A FRÉCHET-URYSOHN SPACE TO BE SEQUENTIALLY COMPACT

  • Hong, Woo-Chorl
    • Communications of the Korean Mathematical Society
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    • v.24 no.1
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    • pp.145-152
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    • 2009
  • In this paper, we introduce a new property of a topological space which is weaker than sequential compactness and give some necessary and sufficient conditions for a $Fr{\acute{e}}chet$-Urysohn space with the property to be sequentially compact.

A Study on the Preliminary Classification System for the Development of the Application Model of Closed School Facilities - Focused on the Comparison of Public Design Indicators with Pre-research - (폐교시설의 활용모형 개발을 위한 예비 분류체계 도출 연구 - 선행연구와 공공 디자인지표의 비교를 중심으로 -)

  • Kim, Jae-young;Lee, Jong-kuk
    • Youth Facilities and Environment
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    • v.17 no.1
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    • pp.131-141
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    • 2019
  • The purpose of this study is to derive and type utilization indexes by comparing public design indicators with preceding studies related to closed school facilities, and to derive preliminary classification systems through a correlation review between indicators. Pre-research was conducted in the scope of academic papers, academic journals, research reports, and special act for promoting the utilization of closed school assets. Public design indicators were set in the scope of domestic design guidelines, the Seoul city public design assessment system, the 'Good Building' designation system, and the UK Design Quality Index (DQI). and the design review of the British architects. First of all, the research method looked at laws, procedures and utilization of closed schools, and reviewed the preceding study and domestic and international public design indicators sequentially. Next, the association was reviewed through a comparison between the preceding study and the public design indicators, and a preliminary classification system for the use of closed schools was derived from this.

A Study on a In-mold Packaging Process using Injection Molding (사출성형을 이용한 마이크로 채널의 패키징 공정에 관한 연구)

  • Lee, Kwan-Hee;Park, Duck-Soo;Yoon, Jae-Sung;Yoo, Yeong-Eun;Choi, Doo-Sun;Kim, Sun-Kyoung
    • Proceedings of the KSME Conference
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    • 2008.11a
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    • pp.1821-1824
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    • 2008
  • A novel in-mold packaging process has been developed to manufacture devices with closed channels. In this unified process, fabrication of open channels and forming the rigid cover on top of them are sequentially integrated in the same mold. The entire process is comprised of two phases. In the first phase, the open channels are fabricated under an exquisitely controlled temperature and pressure using the conventional micro injection molding technology. In the second phase, the closed channels are fabricated by conducting the injection molding process using the molded structure with the open channels as a mold insert. As a result, the in-mold technology can eliminate the bonding processes such as heating, ultrasonic or chemical processes for cohesion between the channel and the cover, which have been required in conventional methods.

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