• Journal of the Korea Society of Computer and Information
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• v.1 no.1
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• pp.189-194
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• 1996

Several fuzzy separation axioms have been defined and Investigated by many authors. The purpose of this note Is to compare fuzzy T, -axioms due to Ganguly and saha with ones due to Mutton and Reilly.

• Education of Primary School Mathematics
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• v.17 no.3
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• pp.253-263
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• 2014

In this paper we review an axiomatic definition of the area of plane figures with area axioms, discuss what the area axioms mean, and analyze the contents about the area of plane figures in elementary school mathematics from the view point of area axioms. So we evaluate which aspects of the concept of area are emphasized or deemphasized in the current elementary school mathematics textbook.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.59-76
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• 2011

Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.115-127
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• 2009

In the present paper we introduce and study L-pre-$T_0$-, L-pre-$T_1$-, L-pre-$T_2$ (L-pre-Hausdorff)-, L-pre-$T_3$ (L-pre-regularity)-, L-pre-$T_4$ (L-pre-normality)-, L-pre-strong-$T_3$-, L-pre-strong-$T_4$-, L-pre-$R_0$-, L-pre-$R_1$-separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the "$\bigwedge$" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.9 no.5
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• pp.7-13
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• 2010

Main starting valve is one of the main parts in the control system of diesel engines, purposed for starting main engines. It is composed of ball valve, check valve, actuator, etc. The design axioms provide a general framework for design methodology. Two axioms are independence axiom and information axiom. These axioms can be applied to all design process in a general way. The first axiom is introduced to analyze and evaluate the design of a main starting valve. The design parameters(DPS) are determined sequentially by considering the independence axiom. For the structural design of a main starting valve, the strength is calculated by using finite element method. In addition, the strength of its actuator piston is evaluated.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.709-727
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• 2018

Here we have studied the ideas of $g^*$-closed sets, $g{\bigwedge}_{{\tau}^-}$ sets and ${\lambda}^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied some separation axioms like $T_{\frac{\omega}{4}}$, $T_{\frac{3\omega}{8}}$, $T_{\omega}$ in Alexandroff spaces and also have introduced a new separation axiom namely $T_{\frac{5\omega}{8}}$ axiom in this space.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.433-450
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• 2009

We introduce a new concept of intuitionistic fuzzy topological subspace, which coincides with the usual concept of intuitionistic fuzzy topological subspace due to Samanta and Mondal [18] in the case that $\mu=X_A$ for A $\subseteq$ X. Also, we introduce and study some concepts such as continuity, separation axioms, compactness and connectedness in this sense.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.723-736
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• 1999

The paper is devoted to generalizations of continuity of set-valued mappings and some properties of hypertopologies on the collection of some subsets of a topological space. It is also dedicated to continuous selection theorems without relatively higher separation axioms. More precisely, we give characterizations of $\lambda$-collectionwise normality using continuous functions as in Michael's papers.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.175-181
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• 2017

In this paper, we introduce a notion of cleanly covered topological spaces along with two strong separation axioms. Some properties of cleanly covered topological spaces are obtained in term of maximal open sets including some similar properties of a topological space in term of maximal closed sets. Two strong separation axioms are also investigated in terms of minimal open and maximal closed sets.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.311-322
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• 2011

In this paper, we generalize the definition of a closure operator for a finite matroid to a pi-space and obtain the corresponding closure axioms. Then we discuss some properties of pi-spaces using the closure axioms and prove the non-existence for the dual of a pi-space. We also present some results on the automorphism group of a pi-space.