Posts Tagged ‘topology’

5 A Day

Thursday, February 28th, 2008

 Yes! I got bazaar working :) Finally, I can start reporting my 5 bugs a day.

Anyway, in regards to the topology problem, my professor is programming some crazy optimized shiz in Python. I figure my only chance to one up him (and multitask) is to write it in Common Lisp. Since that’s what I’m going to be writing my project for Programming Languages in, it’ll be great experience. So far, I’m thinking I’ll be able to take advantage of lists and cons to construct each possible topology. I’ve got a whiteboard in the Math Department Lounge covered with some ideas, so progress is being made.


My 5 today: #192061 (cupsys), #52579 (gstreamer0.10), #188129 (ubuntu), #188097 (nautilus-cd-burner), #190499 (ubuntu)
Do 5 a day - every day! https://wiki.ubuntu.com/5-A-Day

Ubuntu Mobile

Tuesday, February 26th, 2008

Ubuntu Mobile’s finally released!

In personal news, my Topology professor is challenging me to create a more efficient Python program that deals with this problem from our Topology homework:

The set consisting of two elements {a, b} can be given four different topologies:
1. {∅, {a, b}} – The indiscrete topology
2. {∅, {a}, {b}, {a, b}} – The discrete topology
3. {∅, {a}, {a, b}}
4. {∅, {b}, {a, b}}
Each of these is a topology on {a, b} because each one includes {a, b} and is closed
under ∩ and . There are no other topologies on {a, b} because any other set of subsets
would fail to include ∅ or {a, b}.
Determine all of the topologies on the three element set {a, b, c}. Remember that a
topology on X is a set of subsets of X. There are 23 subsets of X. So there are at 3
most 22 = 256 possibilities, most of which fail to be topologies. Any topology must
include ∅ and {a, b, c}. So this cuts down the search. In particular, since we have
no choice but to include these two subsets, the actual subsets of {a, b, c} that are
“up for grabs” are only the remaining 23 − 2 of them. That is, you only need to check 3
22 −2 = 64 possibilities. Even for these, many will fail to be topologies. For example,
τ = {∅, {a}, {b}, {c}, {a, b, c}} is not a topology because {a} ∈ τ and {b} ∈ τ but
{a} ∪ {b} ∈/ τ.

Set theory… brutal.