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 2010 to 2016
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
Teaching methods:	full-time

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

Opinion survey results Examination dates Schedule Noticeboard

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.

Literature - Czech

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

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

2. J.L. Kelley, General Topology, Van Nostrand 1955.

3. P.T. Johnstone, Stone Spaces, Cambridge University Press 1982.

Syllabus -

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

Partial order, suprema and infima. Monotone maps, adjunction. Fixed-point theorems, applications.

Lattices and semilattices, 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.