On the continuity and monotonicity of restrictions of connected functions
ON TEACHER EDUCATION AND ON KEY PROBLEMS OF TEACHING MATHEMATICS
Professor Z. Krygowska in her article, opening the frst issue of the PTM (Polish Mathematical Society) journal Didactics of mathematics (Dydaktyka Matematyki), (Krygowska, 1981) noted that the teacher and his preparation, and thus the problems of teaching mathematics, are never ahistorical. We live here and now, our pupils (students, doctoral students) are immersed in the contemporary time and in the current form of being. The Internet, computer games, the considerable computational capabilities...
On rings of Darboux functions
On the entropy of Darboux functions
We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.
On functions with the set of discontinuity points belonging to some -ideal
On some properties of the spaces of almost continuous functions.
On a K. M. Garg's problem in respect to Darboux functions
On Darboux points and the perfectly closed class of functions
Minimum edukacji matematycznej przyszłych nauczycieli. Kultura matematyczna
Trajectories, first return limiting notions and rings of -connected and iteratively -connected functions
In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted ) contained between the families (widely described in literature) of Darboux Baire 1 functions () and connectivity functions (). The solutions to our problems are based, among other, on the suitable construction of the ring,...
On Świątkowski Functions
Minimum wiedzy matematycznej nauczyciela matematyki oraz projekt organizacji procesu nauczania na nauczycielskich studiach uniwersyteckich
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