Subjects

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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
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	prof. RNDr. Aleš Pultr, DrSc.
Teacher(s):	prof. RNDr. Aleš Pultr, DrSc.
Class:	Informatika Mgr. - Diskrétní modely a algoritmy
Classification:	Informatics > Discrete Mathematics
Pre-requisite :	NMAI064

Opinion survey results Examination dates Noticeboard

Annotation -

Partial order, special partial orders in computer science. DCPOs, domains. Continuous and algebraic posets. Introduction to topology.

Last update: T_KAM (24.03.2004)

Course completion requirements -

Oral exam.

Last update: Kynčl Jan, doc. Mgr., Ph.D. (04.06.2019)

Literature -

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

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

Requirements to the exam -

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.

Last update: Kynčl Jan, doc. Mgr., Ph.D. (04.06.2019)

Syllabus -

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.

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