Introduction to general topology - ALGV00048

• Title: Úvod do obecné topologie
• Guaranteed by: Department of Logic (21-KLOG)
• Faculty: Faculty of Arts
• Actual: from 2020
• Semester: both
• Points: 0
• E-Credits: 5
• Hours per week, examination: 2/1, Ex [HT]
• Capacity: winter:unknown / unknown (unknown); summer:unknown / unknown (unknown)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: English
• Teaching methods: full-time
• Additional information: http://jonathan.temno.eu/teaching/ALGV00048.html
• Note: course can be enrolled in outside the study plan; enabled for web enrollment; you can enroll for the course in winter and in summer semester
• Guarantor: Mgr. Jonathan Verner, Ph.D.

Annotation

English

The course is devoted to the basics of General topology. A rough syllabus follows:

1. The definition of a topology, closed and open sets, basis of a topology, local basis at a point, density
2. Continuous mappings, projectively and inductively generated topologies
3. Separation axioms, Urysohn's lemma, Tietze's theorem, Jones' lemma, linearly ordered spaces, Tykhonoff's plank, The Sorgenfrey line
4. Products of topological spaces, Hewitt-Marczewski-Pondyczéry Theorem, Diagonal lemma, The Tykhonoff cube, The Cantor cube
5. Compactness

Last update: Verner Jonathan, Mgr., Ph.D. (08.03.2016)

Czech

Kurz je věnovaný základům Obecné topologie. Hrubý syllabus:

1. Definice topologie, uzavřené a otevřené množiny, báze topologie, lokální báze topologie v bodě, hustota
2. Spojitá zobrazení, projektivně a induktivně generovaná topologie
3. Oddělovací axiomy, Urysohnovo lemma, Tietzeho věta, Jonesovo lemma, Lineárně uspořádané prostory, Tychonovův plank, Sorgenfreyova přímka
4. Součiny topologických prostorů, Věta Hewitt-Marczewski-Pondyczéry, Diagonální lemma, Tychonovova kostka, Cantorova kostka,
5. Kompaktnost,

Last update: Verner Jonathan, Mgr., Ph.D. (08.03.2016)