(in Polish) Topologia przestrzeni funkcyjnych

General data

Course ID:	1000-1M20TPF
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	(unknown)
Name in Polish:	Topologia przestrzeni funkcyjnych
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Requirements:	Topology I 1000-113bTP1a
Prerequisites:	General topology 1000-135TOG
Mode:	Classroom Remote learning
Short description:	The aim of this course is to introduce students to the theory of topological function spaces endowed with the topology of pointwise convergence and show selected lines of research in this area.
Full description:	The actual plan of the lecture will depend on students' background in topology. It may cover some of the following topics: Filters and ultrafilters; Cartesian products and the Tychonoff theorem; Basic cardinal invariants and their properties; Topologies on the set of continuous functions; Spaces of the form C_p(X), i.e. spaces of continuous functions equipped with the pointwise convergence topology; Borel complexity of C_p(X) spaces; The Baire property in C_p(X) spaces; Factorization theorems; Dual space; Linear homeomorphisms and homeomorphisms of C_p(X) spaces; Baire class one functions; Rosenthal, Eberlein and Corson compact spaces.
Bibliography:	J. van Mill, The Infinite-Dimensional Topology of Function Spaces, Elsevier, 2001. A. Arhangel'skii, Topological Function Spaces}, Kluwer Academic Publishers, 1992. S. Todorcevic, Topics in Topology, Springer, 1997. V. Tkachuk, A $C_p$-Theory Problem Book, vol. 1--4, Springer, 2010--2016.
Learning outcomes:	A student knows and understands basic theorems and and techniques in the theory of topological function spaces: He or she knows selected lines of research in the area.
Assessment methods and assessment criteria:	Final Exam

This course is not currently offered.

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