(in Polish) Topologia przestrzeni funkcyjnych 1000-1M20TPF
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.
Type of course
Mode
Remote learning
Requirements
Prerequisites
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 criteria
Final Exam
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.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: