• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.93-102
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• 2022

The impact of programming languages in the research sector has helped lot of researchers to broaden their view and extend their work without any limitation. More importantly, even the complex problems can be solved in no matter of time while converting them into a programming language. This convenience provides upper hand for the researchers as it places them in a comfort zone where they can work without much stress. With this context, we have converted the research problems in Topology into programming language with the help of Python. In this paper, we have developed a Python program to find the weaker form of closed sets namely alpha closed set, semi closed set, pre closed set, beta closed set and regular closed set.

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.21-30
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• 1992

• East Asian mathematical journal
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• v.24 no.4
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• pp.317-328
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• 2008

In this paper we introduce ${\pi}G{\alpha}$-LC sets, ${\pi}G{\alpha}-LC^*$ sets and ${\pi}G{\alpha}-LC^{**}$ sets and different notions of generalizations of continuous functions in topological space and discuss some of their properties. Further we prove pasting lemma for ${\pi}G{\alpha}-LC^{**}$ continuous functions and ${\pi}G{\alpha}-LC^{**}$ irresolute functions.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.1-9
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• 2011

The notion of ${\tilde{g}}{\alpha}$-closed sets in a topological space introduced by R. Devi and A. selvakumar [2]. In this paper, we introduce the concept of ${\tilde{g}}{\alpha}$-US spaces by utilizing ${\tilde{g}}{\alpha}$-open sets and study the basic properties of this space.

• Journal of applied mathematics & informatics
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• v.2 no.2
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• pp.83-95
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• 1995

Given a closed subset of the family $S^{*}(\alpha)$ of functions starlike of order $\alpha$, a continuous Frechet differentiable functional J, is constructed with this collection as the solution set to the extremal problem ReJ(f) over $S^{*}(\alpha)$. The support points of $S^{*}(\alpha)$ is completely characterized and shown to coincide with the extreme points of its convex hulls. Given any finite collection of support points of $S^{*}(\alpha)$ a continuous linear functional J, is constructed with this collection as the solution set to the extremal problem ReJ(f) over $S^{*}(\alpha)$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.1013-1018
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• 2009

Let * be an e.a.b. star operation on an integrally closed domain D, and let $K\gamma$(D, *) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping $D_{\alpha}{\mapsto}K{\gamma}(D_{\alpha},\;{\upsilon})$ is a bijection from the set {$D_{\alpha}$} of *-linked overrings of D into the set of overrings of $K{\gamma}(D,\;{\upsilon})$. This is a generalization of [5, Proposition 32.19] that if D is a Pr$\ddot{u}$fer domain, then the mapping $D_{\alpha}{\mapsto}K_{\gamma}(D_{\alpha},\;b)$ is a one-to-one mapping from the set {$D_{\alpha}$} of overrings of D onto the set of overrings of $K_{\gamma}$(D, b).

• East Asian mathematical journal
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• v.27 no.3
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• pp.261-271
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• 2011

In this paper, fuzzy ${\alpha}^*$-set, fuzzy C-set, fuzzy AB-set, fuzzy t-set, fuzzy B-set, etc., are introduced in the sense of Sostak [12] and Ramadan [9]. By using these sets, a decomposition of fuzzy continuity and complete fuzzy continuity are provided. Characterization of smooth fuzzy extremally disconnected spaces is also obtained in this connection.

• Honam Mathematical Journal
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• v.28 no.2
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• pp.241-259
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• 2006

Using the concept of interval-valued fuzzy (IVF) sets, the notions of IVF semiopen (semiclosed) sets, IVF preopen (preclosed) sets and IVF $\alpha$-open ($\alpha$-closed) sets are introduced, and interrelations are investigated. Also, the concepts of IVF open mappings, IVF preopen mappings, IVF semiopen mappings and IVF $\alpha$-open mappings are introduced, and interrelations are discussed.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.115-124
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• 2011

In this paper, some fuzzy fixed point theorems for fuzzy mappings are established by considering the nonempty closed $\alpha$-cut sets. Some importance observations are also discussed. Our results clearly extend, generalize and improve the corresponding results in the literatures, which have given most of their attention to the class of fuzzy sets with nonempty compact or closed and bounded $\alpha$-cut sets.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.307-331
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• 2010

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy ${\gamma}$-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy ${\gamma}$-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy ${\gamma}$-open set is discussed.