• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.151-159
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• 1997

Observing that for any dense weakly Lindelof subspace of a space Y, X is $Z^{#}$ -embedded in Y, we show that for any weakly Lindelof space X, the minimal Cloz-cover ($E_{cc}$(X), $z_{X}$) of X is given by $E_{cc}$(X) = {(\alpha, \chi$) : $\alpha$ is a G(X)-ultrafilter on X with $\chi\in\cap\alpha$}, $z_{X}$=(($\alpha, \chi$))=$\chi$, $z_{X}$ is $Z^{#}$ -irreducible and $E_{cc}$(X) is a dense subspace of $E_{cc}$($\beta$X).

• Journal of the Korean Institute of Telematics and Electronics
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• v.12 no.4
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• pp.21-27
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• 1975

In this paper, a procedure for deriving of multiple fault detection test sets is presented for fan-out reconvergent combinational logic networks. A fan-out network is decomposed into a set of fan-out free subnetworks by breaking the internal fan-out points, and the minimal detecting test sets for each subnetwork are found separately. And then, the compatible tests amonng each test set are combined maximally into composite tests to generate primary input binary vectors. The technique for generating minimal test experiments which cover all the possible faults is illustrated in detail by examples.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.45-51
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• 2002

Observing that a realcompactification Y of a space X is Wallman if and only if for any non-empty zero-set Z in Y, $Z{\cap}Y{\neq}{\emptyset}$, we will show that for any pseudo-Lindel$\ddot{o}$f space X, the minimal quasi-F $QF({\upsilon}X)$ of ${\upsilon}X$ is Wallman and that if X is weakly Lindel$\ddot{o}$, then $QF({\upsilon}X)={\upsilon}QF(X)$.

• East Asian mathematical journal
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• v.30 no.1
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• pp.63-67
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• 2014

Observing that for any P'-space X, ${\Lambda}vX$ is a P'-space if vX is a weakly Lindel$\ddot{o}$f space, (${\Lambda}vX{\times}{\Lambda}Y$, ${\Lambda}_X{\times}{\Lambda}_Y$) is the minimal basically disconnected cover of $X{\times}Y$ for a countably locally weakly Lindel$\ddot{o}$f space Y.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.709-718
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• 2002

Observing that each Tychonoff space X has the minimal basically disconnected cover (ΛX, Λ$\sub$X/) and the .realcompact-ification $\upsilon$X, we introduce a concept of stable $\sigma$Z(X)#-ultrafilters and give internal characterizations of Tychonoff spaces X for which Λ($\upsilon$X) : $\upsilon$(ΛX).

• Journal for History of Mathematics
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• v.16 no.1
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• pp.73-78
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• 2003

Observing that if f: $Y{\leftrightarro}$Χ is a covering map and Χ is a countably locally weakly Lindelof space, then Y is countably locally weakly Lindelof and that every dense countably weakly Lindelof subspace of a basically disconnected space is basically disconnected, we show that for a countably weakly Lindelof space Χ, its minimal basically disconnected cover ${\bigwedge}$Χ is given by the filter space of fixed ${\sigma}Ζ(Χ)^#$- ultrafilters.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.161-168
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• 2002

We show that if the Stone-Cech compactification of $\textit{AX}$ and the minimal basically disconnected cove. of $\beta$Χ we homeomorphic and every real $\sigma$$Z(X)^#$-ultrafilter on X has the countable intersection property, then there is a covering map from $\nu$(ΛΧ) to $\nu$Χ and every real $\sigma$$Z(X)^#$-ultrafilter on Χ has the countable intersection property if and only if there is a homeomorphism from the Hewitt realcompactification of ΛΧ to the minimal basically disconnected space of $\nu$Χ.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.117-124
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• 1993

In this paper, we introduce a concept of quasi $O_{z}$ -spaces which generalizes that of $O_{z}$ -spaces. Indeed, a completely regular space X is a quasi $O_{z}$ -space if for any regular closed set A in X, there is a zero-set Z in X with A = c $l_{x}$ (in $t_{x}$ (Z)). We then show that X is a quasi $O_{z}$ -space iff every open subset of X is $Z^{#}$-embedded and that X is a quasi $O_{z}$ -spaces are left fitting with respect to covering maps. Observing that a quasi $O_{z}$ -space is an extremally disconnected iff it is a cloz-space, the minimal extremally disconnected cover, basically disconnected cover, quasi F-cover, and cloz-cover of a quasi $O_{z}$ -space X are all equivalent. Finally it is shown that a compactification Y of a quasi $O_{z}$ -space X is again a quasi $O_{z}$ -space iff X is $Z^{#}$-embedded in Y. For the terminology, we refer to [6].[6].

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1001-1011
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• 2018

We introduce some variants of the finite Ramsey theorem. The variants are based on a refinement of homogeneity. In particular, they cover homogeneity, minimal homogeneity, end-homogeneity as special cases. We also show how to obtain upper bounds for the corresponding Ramsey numbers.

• Journal for History of Mathematics
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• v.11 no.2
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• pp.83-90
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• 1998

Observing that for any compact space X, the minimal basically disconnected cover ${\bigwedge}Λ_X$ : ${\bigwedge}Λ_X{\leftrightarro}$ is ${\sigma}Z^#$-irreducible, we will show that the projective objects in the category of compact spaces and ${\sigma}Z^#$-irreducible maps are precisely basically disconnected spaces.