• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.185-190
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• 1991

The concept of "almost invertibility modulo closed ideals" in L(X, Y) was introduced, implicitly, by Robin Harte [1, Theorem 3.9.5]. The aims of this note are to make the formal definition of "almost left and right invertible modulo closed ideals" operators and show that they form open sets.they form open sets.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.79-85
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• 2000

In this paper, we have an affirmative solution of G. Godini's open question ([3]): If a normed almost linear space Y is complete, is the normed almost linear space B(X, (Y,C)) complete?

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.4
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• pp.525-529
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• 2011

We introduce the concept of IVF almost ${\alpha}$-continuity and investigate characterizations for such mappings on the interval-valued fuzzy topological spaces. We study the relationships between IVF almost ${\alpha}$-continuous mappings and another types of IVF continuous mappings.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.49-57
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• 2007

Using the idea of degree of openness and degree of nonopenness, Coker and Demirci [5] defined intuitionistic fuzzy topological spaces in Sostak's sense as a generalization of smooth topological spaces and intuitionistic fuzzy topological spaces. M. N. Mukherjee and S. P. Sinha [10] introduced the concept of fuzzy irresolute maps on Chang's fuzzy topological spaces. In this paper, we introduce the concepts of fuzzy (r,s)-irresolute, fuzzy (r,s)-presemiopen, fuzzy almost (r,s)-open, and fuzzy weakly (r,s)-continuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. Using the notions of fuzzy (r,s)-neighborhoods and fuzzy (r,s)-semineighborhoods of a given intuitionistic fuzzy points, characterizations of fuzzy (r,s)-irresolute maps are displayed. The relations among fuzzy (r,s)-irresolute maps, fuzzy (r,s)-continuous maps, fuzzy almost (r,s)-continuous maps, and fuzzy weakly (r,s)-cotinuous maps are discussed.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.205-210
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• 2001

We give a characterization of regular operators that allows us to prove that a bounded operator acting between Banach spaces is almost regular if and only if it is regular, solving an open problem in [5]. As an application, we show that some operators in the closure of the set of all regular operators are regular.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.141-148
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• 2010

We introduce the concept of fuzzy almost r-M continuous function on fuzzy r-minimal structures and investigate characterizations and properties for such a function.

• Journal of The Korean Astronomical Society
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• v.35 no.2
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• pp.87-95
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• 2002

We have conducted VI CCD photometry of the open cluster NGC 6819 in order to understand the effects of dynamical evolution in old open clusters. Our photometry covers 18' $\times$ 18' on the sky, centered on the cluster, which seems to cover the whole cluster field. Our photometry reaches down to V $\approx$ 20.5, which allows us to analyze the luminosity function and spatial distribution of stars brighter than Mv $\approx$ 8.5. There is a clear evidence for mass segregation in NGC 6819, i.e., the giants and upper main-sequence stars are concentrated in the inner regions, whereas the lower main-sequence stars distribute almost uniformly throughout the cluster. The luminosity function of the main-sequence stars of NGC 6819 is almost flat. The flat luminosity function indicates that a large number of low mass stars has escaped from the cluster unless its initial mass function is much different from the Salpeter type (${\phi}(m){\propto} m^{-(1+x)},x = 1.35$).

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.291-296
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• 2011

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.44-48
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• 2011

The purpose of this paper is to introduce and investigate the concept of fuzzy almost r-minimal continuous function between fuzzy minimal spaces and fuzzy topological spaces. Particularly, we investigate characterizations for the fuzzy almost r-minimal continuity by using generalized fuzzy r-open sets.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.91-102
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• 1986

A topological space (X,.tau.) is called invertible [7] if for each proper open set U in (X,.tau.) there exists a homoemorphsim h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. Doyle and Hocking [7] and Levine [13], as well as others have investigated properties of invertible spaces. Recently, Crosseley and Hildebrand [5] have introduced the concept of semi-invertibility, which is weaker than that of invertibility, by replacing "homemorphism" in the definition of invertibility with "semihomemorphism", A space (X,.tau.) is said to be semi-invertible if for each proper semi-open set U in (X,.tau.) there exists a semihomemorphism h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. The purpose of the present article is to introduce the class of almost-invertible spaces containing the class of semi-invertible spaces and to investigate its properties. One of the primary concerns will be to determine when a given local property in an almost-invertible space is also a global property. We point out that many of the results obtained can be applied in the cases of semi-invertible spaces and invertible spaces. For example, it is shown that if an invertible space (X,.tau.) has a nonempty open subset U which is, as a subspace, H-closed (resp. lightly compact, pseudocompact, S-closed, Urysohn, Urysohn-closed, extremally disconnected), then so is (X,.tau.).hen so is (X,.tau.).