• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.113-120
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• 2012

In this paper we study various properties of the fuzzy linear maps over the fuzzy quotient spaces. In particular we obtain some exact sequences of the fuzzy linear maps over the fuzzy quotient spaces.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.61-70
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• 2017

In this paper, we introduce the concept of statistically sequentially quotient map which is a generalization of sequence covering map and discuss the relation with covering maps by some examples. Using this concept, we give an affirmative answer for a question by Fucai Lin and Shou Lin.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.383-391
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• 2019

For a DM stack 𝓧, Chen, Marcus and Úlfarsson ([3]) constructed a stack 𝓖_𝓧 of gerbes in 𝓧 that plays a key role in their setting up the theory of very twisted stable maps to 𝓧. This stack is realized as a rigidification of the stack S_𝓧 of subgroups of the inertia stack of 𝓧. In this article, we show that when 𝓧 is a quotient stack, the stacks 𝑺_𝓧 and 𝓖_𝓧 are also quotient stacks.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1087-1094
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• 1996

In this paper, we introduce the notion of the n-th pretopological modification. Also, we find some properties which hold between convergence quotient maps and n-th pretopological modifications.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.33-40
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• 1996

A convergence structure defined by Kent [4] is a correspondence between the filters on a given set X and the subsets of X which specifies which filters converge to points of X. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on X. Thus, a convergence structure may be regarded as a generalization of a topology. With a given convergence structure q on a set X, Kent [4] introduced associated convergence structures which are called a topological modification and a pretopological modification. (omitted)

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.541-548
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• 2008

For a completely bounded linear maps between operator spaces, we introduce numbers which measure the degree of injectivity and subjectivity. The number measuring the injectivity is an operator space analogue of the minimum modulus of a linear map in normed spaces.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.267-280
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• 2023

In this article, we show that the family of all 𝓘^𝒦-open subsets in a topological space forms a topology if 𝒦 is a maximal ideal. We introduce the notion of 𝓘^𝒦-covering map and investigate some basic properties. The notion of quotient map is studied in the context of 𝓘^𝒦-convergence and the relationship between 𝓘^𝒦-continuity and 𝓘^𝒦-quotient map is established. We show that for a maximal ideal 𝒦, the properties of continuity and preserving 𝓘^𝒦-convergence of a function defined on X coincide if and only if X is an 𝓘^𝒦-sequential space.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.353-361
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• 2024

We consider 𝒩 to be a 3-prime field and 𝒫 to be a prime ideal of 𝒩. In this paper, we study the commutativity of the quotient near-ring 𝒩/𝒫 with left multipliers and derivations satisfying certain identities on 𝒫, generalizing some well-known results in the literature. Furthermore, an example is given to illustrate the necessity of our hypotheses.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.991-1004
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• 2019

Firstly we consider preorders (not necessarily partial orders) on a canonical quotient of the set of the homotopy classes of continuous maps between two spaces induced by a certain equivalence relation ${\sim}_{{\varepsilon}R}$. Secondly we apply it to a classification of orientable fibrations over Y with fibre X. In the classification theorem of J. Stasheff [22] and G. Allaud [3], they use the set $[Y,\;Baut_1X]$ of homotopy classes of continuous maps from Y to $Baut_1X$, which is the classifying space for fibrations with fibre X due to A. Dold and R. Lashof [11]. In this paper we give a classification of fibrations using a preordered set (abbr., proset) structure induced by $[Y,\;Baut_1X]_{{\varepsilon}R}:=[Y,\;Baut_1X]/{\sim}_{{\varepsilon}R}$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.657-662
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• 2001

It is proved that if for each n, $1\leqp_n\leq2 \;and \;the(p_n, p’_n)$ Clarkson inequality holds in each Banach space X$_{n}$ then the (t, t’) Clarkson inequality holds in ($\sum^\infty_{n=1}\; X_n)_r, \;the \ell^r-sum \;of\; X_n’s,\; where\; 1\leqr<\infty,\; t=min{p, r, r’} \;and \;p = \;inf{p_n}.$ The (p, p’) Clarkson inequality is preserved by quotient maps and a new proof of a Takahashi-Kato theorem stating that the (p, p’) Clarkson inequality holds in a Banach space X if and only if it holds in its dual space $X_*$ is given.n.