In this study, it was aimed to test whether there were differences and failures between the definitions that lecturers desired to form in students minds and the definitions that students described, and if so, to investigate the reasons of those differences and failures based on the fundamental topologic concepts topic from students perspectives. A case study research design was adopted in the study and it was conducted with 99 students of elementary mathematics teaching department. The data were gathered via three ways, Knowledge Test, Unstructured Focus Group Interview and Structured Interview Form, and were analyzed with descriptive and content analysis methods. As a result, it was observed that there were considerably big differences between the formal definitions of that the lecturers used in teaching and the definitions defined by the students. According to the students, these differences and failures stemmed from following reasons: students living difficulties in stating their ideas with the mathematical language, their prior learning habits, their negative ideas about the necessity of the concepts, their lecturers use of the language, their lecturers neglecting individual differences in teaching, their poor working habits and abstractness of the topics
Key words: topologic concepts, formal definition, loss of information, definitions formation
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