### THE CONTINUITY AND THE IMPORTANT THEOREMS IN THE TOPOLOGICAL KNOWLEDGE SPACES

#### Abstract

In this study my goal is to define the concept of continuity and to uncover its important in the topological knowledge space. Moreover, I introduce pedagogically sound concept of continuity for the topological knowledge structure modeling a students’ learning and the important theorems are proofed. Indeed, some definitions are presented and theorems are proofed. Consequently, it is proofed that in the topological knowledge spaces as a result of continuity well-graded, learning smooth and accessible have been kept in continuity. Thus, a minimal set of requirements for a knowledge structure whose emphasis is the modeling of students' learning can be described as a minimal set of requirements for making up a different knowledge space.

**Keywords:** Continuity, topological knowledge, topological spaces

**References**

Cosyn, E., & Uzun, H. B. (2009). Note on two necessary and sufficient axioms for a well-graded knowledge space. *Journal of Mathematical Psychology*, *53*, 1, 40-42.

Doignon, J. P., & Falmagne, J. C. (1985). Spaces for the assessment of knowledge. *International Journal of Man-Machine Studies,* *23*, 175–196.

Doignon, J. P., & Falmagne, J. C. (1999). *Knowledge spaces*., Berlin, Heidelberg, NY: Springer-Verlag.

Falmagne, J. C., & Doignon, J. P. (1988). A Markovian procedure for assessing the state of a system. *Journal of Mathematical Psychology*, *32*, 232–258.

Falmagne, J. C. (1989). A latent trait theory via a stochastic learning theory for a knowledge space. *Psychometrika,* *53*, 283–303.

Falmagne, J. C. (1993). Stochastic learning paths in a knowledge structure. *Journal of Mathematical Psychology*, *37*, 489-512.

Koppen, M. (1998). On alternative representations for knowledge spaces. *Mathematical Social Sciences*, *36*, 127–143.

Kreyszig, E. (1989). *Introductory functional analysis with applications*. New York: Wiley Classics Library Edition Published.

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