This is a lecture on the properties of open sets in finite-dimensional Euclidean space by Dr Joel Feinstein from his second-year module on Mathematical Analysis. This material is suitable for those who already know the definitions of open set and of the interior of a set in finite-dimensional Euclidean space.
In this session Dr Feinstein shows that finite unions and intersections of open sets are open, and then discusses infinite unions and intersections. It turns out that infinite unions of open sets are still open, but that infinite intersections of open sets need not be open any more.
See also Dr Feinstein's blog, Explaining Mathematics, http//explainingmaths.wordpress.com/
@MrThatstheguy
The whole module can be viewed or downloaded from the University of Nottingham's uNoW site. These lectures are also being released on YouTube in a separate Mathematical Analysis playlist, as well as on Nottingham's iTunes U area (free iTunes software required).
See my blog Explaining Mathematics for more links.
JoelFeinstein 6 months ago in playlist Mathematics
@MrThatstheguy
You can download the whole of this module (including videos, annotated slides, question sheets and solutions) from u-Now, the University of Nottingham's Open Educational Repository.
See "My Screencasts" on my blog Explaining Mathematics for links to this and other resources. Joel Feinstein
JoelFeinstein 1 year ago
i cant find your closed set lecture :(
MrThatstheguy 1 year ago