Forthcoming events in this series


Mon, 03 Mar 2014
14:00
C6

Generalised metrisable spaces and the normal Moore space conjecture

Robert Leek
(Oxford)
Abstract

We will introduce a few class of generalised metrisable

properties; that is, properties that hold of all metrisable spaces that

can be used to generalise results and are in some sense 'close' to

metrisability. In particular, we will discuss Moore spaces and the

independence of the normal Moore space conjecture - Is every normal

Moore space metrisable?

Mon, 24 Feb 2014
14:00
C6

Elementary submodels in topology

Richard Lupton
(Oxford)
Abstract

We explore the technique of elementary submodels to prove 
results in topology and set theory. We will in particular prove the 
delta system lemma, and Arhangelskii's result that a first countable 
Lindelof space has cardinality not exceeding continuum.

Mon, 17 Feb 2014
14:00
C6

D-spaces (4): Topological games

Robert Leek
Abstract

 We will introduce 2 types of topological games (Menger and
> Telgársky) and show how the existence or non-existence of winning
> strategies implies certain properties of the underlying topological
> space. We will then show how these, and related properties, interact
> D-spaces.

Mon, 02 Dec 2013
14:00
C6

Diamonds

Richard Lupton
(Oxford)
Abstract

 We take a look at diamond and use it to build interesting 
mathematical objects.

Mon, 18 Nov 2013
14:00
C6

D-spaces: (2.5) Buzyakova's conjecture

Max Pitz
(Oxford)
Abstract

We will finish presenting Nyikos' counterexample to 
Bozyakova's conjecture: If e(Y) = L(Y) for every subspace Y of X, must X 
be hereditarily D?

Mon, 11 Nov 2013
14:00
C6

D-spaces: (2) Interval topologies on trees and Buzyakova's conjecture

Max Pitz
(Oxford)
Abstract

Raushan Buzyakova asked if a space is hereditarily D provided 
that the extent and Lindelöf numbers coincide for every subspace. We 
will introduce interval topologies on trees and present Nyikos' 
counterexample to this conjecture.

Mon, 04 Nov 2013
14:00
C6

D-spaces: (1) Extent and Lindelöf numbers

Robert Leek
(Oxford)
Abstract

This is the first of a series of talks based on Gary 
Gruenhage's 'A survey of D-spaces' [1]. A space is D if for every 
neighbourhood assignment we can choose a closed discrete set of points 
whose assigned neighbourhoods cover the space. The mention of 
neighbourhood assignments and a topological notion of smallness (that 
is, of being closed and discrete) is peculiar among covering properties. 
Despite being introduced in the 70's, we still don't know whether a 
Lindelöf or a paracompact space must be D. In this talk, we will examine 
some elementary properties of this class via extent and Lindelöf numbers.