• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.675-680
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• 2002

Since N. Levin [1] in 1961 defined the weakly continuous function, there is a lot of weakened forms of continuous function. In this paper we consider two forms of the weakened form of continuous function and study the some properties of them.

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

• 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.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.157-160
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• 2011

Main purpose of this note is to construct an example of a continuous one-to-one function f : ${\mathbb{Q}}^*{\rightarrow}{\mathbb{R}}$ whose inverse is nowhere continuous, and to show that the completeness is not necessary for the continuous inverse theorem.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.249-258
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• 2006

The weakened forms of the (${\theta},s$)-continuous function are introduced and their basic properties are investigated in concern with the other weakened continuous function. The open property of a function and the extremal disconnectedness of the spaces are crucial tools for the survey of these functions.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1553-1560
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.124-127
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• 2010

In this paper, we introduce the concepts of fuzzy r-minimal continuous function and fuzzy r-minimal open function between a fuzzy r-minimal space and a fuzzy topological space. We also investigate characterizations and properties for such functions.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.993-1001
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• 2010

In this paper, we introduce the concept of fuzzy weakly r-M continuous function on r-minimal structures and investigate characterizations and properties for such functions.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.489-496
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• 2007

Let g be a continuous function on an interval I which is not constant on any subinterval of I, and let ${\mu}$ be a Borel measure on I. In this paper we give a necessary and sufficient conditions guaranteeing, for the strongly measurable function f on I with values in a Banach space X, the existence of a continuous primitive function F on I with respect to g.

• The Mathematical Education
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• v.57 no.4
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• pp.477-491
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• 2018

In this paper we study in-service teachers' and pre-service teachers' recognition the domain in the problem concerning the continuity of a function. By a questionnaire survey we find out that most of in-service teachers and pre-service teachers are understanding the continuity of a function as explained in high school mathematics textbook, in which the continuity was defined by and focused on comparing the limit with the value of the function. We also notice that this kind of definition for the continuity of a function makes them trouble to figure out whether a function is continuous at an isolated point, and to determine that a given function is continuous on a region by not considering its domain explicitly. Based on these results we made several suggestions to improve for in-service teachers and pre-service teachers to understand the continuity of a function more exactly, including an introduction of a more formal words usage such as 'continuous on a region' in high school classroom.