The aim of studying and bibliography

The main aim of study: Teaching students basic topological structures and their fundamental properties of the objects found in geometry and mathematical analysis.

The general information about the module: Topics discused in the module: topological spaces, metric spaces, bases and subbases, countability, separation axioms, continuity, homeomorphism, topological properties, deformations, knots, compactness, connectedness, complete metric spaces, Brouwer theorem.

Bibliography required to complete the module

Bibliography used during lectures

1	K. Kuratowski	Wstęp do teorii mnogości i topologii	WN PWN.	2004
2	S. Gładysz	Wstęp do topologii	PWN.	1981

Bibliography used during classes/laboratories/others

1	J. Jędrzejewski, W. Wilczyński	Przestrzenie metryczne w zadaniach	Wyd. UŁ.	2007
2	W. Rzymowski	Przestrzenie metryczne w analizie	Wyd. UMCS.	2000

Bibliography to self-study

1	J. Jędrzejowski, W. Wilczyński	Przestrzenie meytryczne w zadaniach	Wyd. UŁ.	2007
2	W. Rzymowski	Przestrzenie metryczne w analizie	Wyd. UMCS.	2000

Basic requirements in category knowledge/skills/social competences

Formal requirements: The student satisfies the formal requirements set out in the study regulations

Basic requirements in category knowledge: Students have achieved learning outcomes: K_W01, K_W02, K_W04, K_W05, K_W06, K_W07 (wg Rozporządzenia MNiSW z dnia 4.11.2011 r. w sprawie wzorcowych efektów kształcenia, załącznik nr 3)

Basic requirements in category skills: Students have achieved learning outcomes: K_U01, K_U02, K_U05, K_U08, K_U09, K_U10, K_U16, K_U23, K_U24 (wg Rozporządzenia MNiSW z dnia 4.11.2011 r. w sprawie wzorcowych efektów kształcenia, załącznik

Basic requirements in category social competences: Students have achieved learning outcomes: K_K01, K_K02, K_K06 (wg Rozporządzenia MNiSW z dnia 4.11.2011 r. w sprawie wzorcowych efektów kształcenia, załącznik nr 3)

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01		lectures, problem exercises	writtten test	K_W01+++ K_W02++ K_W03++ K_W04++ K_W05++ K_W07++ K_U01++ K_U02++ K_U03++ K_U04++ K_U08+++ K_U13++ K_U14+ K_U15+ K_K01++ K_K02++ K_K04+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UU P7S_UW P7S_WG P7S_WK

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
1	TK01	Topological spaces. Metric spaces.	W01, W02, W03, C01, C02, C03	MEK01
1	TK02	Bases, subbases. Countability. Density. Separable spaces. Separation sxioms.	W04, W05, W06, W07, C04, C05, C06, C07
1	TK03	Continuity. Homeomorphism. Topological properties. Deformations. Knots.	W08, W09, W10, C08, C09, C10	MEK01
1	TK04	Compactness. Complete metric spaces. Connectedness.	W11, W12, W13, W14, C11, C12, C13, C14
1	TK05	Brouwer's theorem.	W15, C15	MEK01

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 1)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 14.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 15.00 hours/sem.	contact hours: 45.00 hours/sem.	Finishing/Studying tasks: 5.00 hours/sem. Others: 5.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Exam (sem. 1)	The preparation for an Exam: 50.00 hours/sem.	The written exam: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	see exam
Class	see exam
The final grade	Written test 8 problems - 80 points + points ,The final resulta: [50,60) result E, [60,70) result D, [70,80) result C, [80,90) result B, [90,100] result A.

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: yes

1	J. Górnicki	Sinus i cosinus w akcji	2022
2	J. Górnicki	Wszędzie brak pochodnej	2022
3	J. Górnicki	Fixed point theorems in preordered sets	2021
4	J. Górnicki	Kostka	2021
5	J. Górnicki	Które zgięcie jest naj. . . ?	2021
6	J. Górnicki	O metrykach i kulach	2021
7	R. Bisht; J. Górnicki	Around averaged mappings	2021
8	J. Górnicki	Elementarnie o twierdzeniu Brouwera	2020
9	J. Górnicki	Fibonacci spotyka Banacha	2020
10	J. Górnicki	Infekcja	2020
11	J. Górnicki	Jaki jest kształt wszechświata?	2020
12	J. Górnicki	Leibniz i Calculus	2020
13	J. Górnicki	Odkryj wielokąt!	2020
14	J. Górnicki	On some mappings with a unique fixed point	2020
15	J. Górnicki	Perełka: e^{ipi} + 1 = 0	2020
16	J. Górnicki	Zabawa zapałkami	2020
17	J. Górnicki	Fixed points, multi-valued uniformly Lipschitzian mappings and uniform normal structure	2019
18	J. Górnicki	Kraty	2019
19	J. Górnicki	Kto ma rację?	2019
20	J. Górnicki	Remarks on asymptotic regularity and fixed points	2019
21	J. Górnicki	Ślad ruchomego odcinka	2019