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 has completed undergraduate degree in mathematics or a related (informatics, physics) after addition differences.

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 OEK
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+	X2A_W02++ X2A_W03++ X2A_U01++ X2A_U02+ X2A_U03++ X2A_U05+++ X2A_U06++ X2A_U08+ X2A_U09+ X2A_K01++ X2A_K03+ X2A_K04+ X2A_K06++

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: 10.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 15.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 5.00 hours/sem. Others: 5.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 5.00 hours/sem.	The participation in Advice: 4.00 hours/sem.
Exam (sem. 1)	The preparation for an Exam: 60.00 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: no