Seminar iz topologije

Vodji seminarja: Tina Sovič in Jernej Činč.
Predavanja potekajo ob petkih ob 13:00 v predavalnici 01/20.

Bodoča predavanja

Minula predavanja

Trees and inverse limits of set-valued functions on intervals

Predavateljica: Sina Greenwood (Univerza v Aucklandu, Nova Zelandija)

Povzetek: I will consider inverse limits of sequences of upper semicontinuous set-valued functions on intervals for which the graph of each bonding function is an arc. I will show how to construct any finite tree as such an inverse limit, and one for which each bonding function is one of two specified functions. I will also touch on infinite trees.


Predavatelj: Iztok Banič

Graph-like Continua: Characterizations and Eulerian Loops

Predavatelj: Paul Gartside (University of Pittsburgh, ZDA)

POVZETEK: Locally finite graphs can be compactified, to form the Freudenthal compactification, by adding their ends. This topological setting provides what appears to be the ‘right’ framework for studying locally finite graphs. Indeed, many classical theorems from finite graph theory that involve paths or cycles have been shown to generalize to locally finite, infinite graphs in this topological setting, while failing to extend in a purely graph theoretic context. More recently, compact graphlike spaces were introduced by Thomassen and Vella, as a natural class encompassing graphs, and their Freudenthal compactifications. We present various characterizations of graph-like continua and explore when they are Eulerian.

Connectedness and inverse limits with set-valued functions on intervals

Predavateljica: Sina Greenwood (Univerza v Aucklandu)

An inverse limit with upper semicontinuous set-valued functions on intervals is connected if and only if it does not admit a CC-sequence. I will introduce a related notion, a component base. Using this new tool I will demonstrate how proofs of connectedness theorems can be simplified, and discuss a number of new results on connectedness, in particular, results relating to the size and number of components.

Predavanje bo tokrat izjemoma ob 12.00 v predavalnici 0/80.