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Course, academic year 2022/2023
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Topological and Algebraic Methods - NMAI066
Title: Topologické a algebraické metody
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Aleš Pultr, DrSc.
Class: Informatika Mgr. - Diskrétní modely a algoritmy
Classification: Informatics > Discrete Mathematics
Pre-requisite : NMAI064
Annotation -
Last update: T_KAM (24.03.2004)
Partial order, special partial orders in computer science. DCPOs, domains. Continuous and algebraic posets. Introduction to topology.
Course completion requirements -
Last update: Mgr. Jan Kynčl, Ph.D. (04.06.2019)

Oral exam.

Literature -
Last update: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)

B.A. Davey, H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press 1990.

A Compendium of Continuous Lattices.

J.Picado, A. Pultr, Frames and Locales, Birkhauser (Springer) 2012

Requirements to the exam -
Last update: Mgr. Jan Kynčl, Ph.D. (04.06.2019)

Partially ordered sets, special posets of computer science (DCPO, continuous and algebraic lattices). Scott information systems and domains.

Basics of point-free topology, relations to the classical one, constructive aspects.

Oral exam.

Syllabus -
Last update: prof. RNDr. Aleš Pultr, DrSc. (11.10.2017)

Special lattices, algebraic aspects. Boolean and Heyting algebras.

Partial orders with suprema of directed sets (DCPO), their role in computer science. Continuous and algebraic lattices and posets. Scott information systems and domains. Categories of domains.

Fundamentals of topology. Spaces and continuous maps. Separation axioms. Compactness. Special topologies of computer science (Scott, Lawson).

Fundamentals of point-free topology: concepts and basic facts, relation ot classical topology, constructive aspects.

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