Math 535  General Topology
Fall 2012
Homework 10 Solutions
Problem 1. Let Top denote the category of topological spaces and continuous maps, and
let CHaus denote the category of compact Hausdor topological spaces and continuous maps.
Show that the Stone
o
o
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Joseph Gay Lussacs la
Law of combining volumes: gases will combine in small integer ratios
Avogadro
Equal volumes of different gases at the same temperature and pressure contain equal
numbers of particles
2H2+o22H2O
3H2+N22NH3
Velocity v= dx/dt ;
1.3.4
1.1.1
Conservation of matter and energy
Matter and Energy isnt created/destroyed in chemical reactions
o Energy is conserved
1.1.2
Macroscopic: Big
Nanoscopic: atomic level
1.2.1
Heterogeneous: Not uniformly distributed
o Wood
Homogeneous: Uniformly
Phlogiston
Wood>ash+phlogiston
Metal>calx+phlogiston
Ash was lighter than wood, but calx was heavier than metal
Lavoisier: Studied air and the relation to combustion
Priestly: Found different types of air
Normal: breathable air, supports a flame
Fixed:
Is there a correct way to say things?
Every region of a certain are that speaks a certain language has a different dialect. For example in Iowa
many people pronounce creeks as cricks
What are language norms for, and what effects does it have if someone co
How to Set Up the Machine
You can also install the printer driver by directly specifying the inf file in [Driver]. See "Installing to Use WSD" in the Printer Driver
Installation Guide (HTML manual).
LAN
1
Connecting via a Network
Perform [Network_Setting_
Karin ResendizMedina
20200
10/12/16
Ensayo 1
Creo que la invencin ms importante del siglo XX y el siglo XXI es la electricidad.
Muchas invenciones desde la invencin de electricidad dependen de ello. Los telfonos necesitan
la electricidad para funcionar.
THE UNIVERSITY OF CHICAGO
DEPARTMENT OF ROMANCE LANGUAGES AND LITERATURES
SPANISH 20200 LANGUAGE, HISTORY AND CULTURE II
AUTMN 2016 COURSE SYLLABUS
Spanish Program Coordinator: Janet Sedlar
Office: GatesBlake 213; Office tel: 7737027926; email: janetse
CALENDARIO
Espaol 20200 Otoo 2016
Lunes
Mircoles
Viernes
26 de septiembre de 2016
28 de septiembre de 2016
30 de septiembre de 2016
Captulo 5
El mundo al alcance de un clic
Captulo 5
Semana 2
Semana 1
Introduccin
Presentacin oral y escrita
Tarea para hoy:
chemistry
113/123
Spring 2017
Laboratory Schedule
Week
1
Dates
March 27  31
Experiment
Introductory Week
* Discussion sessions start on Thursday, March 30.
* Discussions on M/T/W start in the second week.
* Deadline for lab section change is Friday, Mar.
Math 535  General Topology
Fall 2012
Final Exam
Name: Solutions
Allowed: The four textbooks, notebooks, printouts of course material, and your own
homework.
Not allowed: Other documents, and any electronic devices (laptops, iPads, smartphones,
cell pho
Math 535  General Topology
Fall 2012
Homework 5 Solutions
Problem 1. Let X be a rstcountable topological space, (xn )nN a sequence in X , and y X
a cluster point of this sequence. Show that there is a subsequence (xnk )kN that converges to y .
Solution.
Math 535  General Topology
Fall 2012
Homework 9 Solutions
Problem 1.
a. Let X be a topological space with nitely many connected components. Show that each
connected component is open in X .
Solution. Let X = X1 . . . Xn be the partition of X into connect
Math 535  General Topology
Fall 2012
Homework 11 Solutions
Problem 1. Let X be a topological space.
a. Show that the following properties of a subset A X are equivalent.
1. The closure of A in X has empty interior: int(A) = .
2. For all nonempty open su
Math 535  General Topology
Fall 2012
Homework 12 Solutions
Problem 1. Consider the open cover U = cfw_B1 (x)xR of R by open balls of radius 1, i.e.
open intervals B1 (x) = (x 1, x + 1). Find a partition of unity on R subordinate to U .
Solution. We will
Math 535  General Topology
Fall 2012
Homework 14 Solutions
Problem 1. Let X be a topological space and (Y, d) a metric space. For each compact subset
K X , consider the pseudometric on C (X, Y ) dened by
dK (f, g ) = sup d (f (x), g (x)
xK
and its associ
Math 535  General Topology
Fall 2012
Homework 13 Solutions
Note: In this problem set, function spaces are endowed with the compactopen topology unless
otherwise noted.
Problem 1. Let X be a compact topological space, and (Y, d) a metric space. Consider
Math 535  General Topology
Fall 2012
Homework 8 Solutions
Problem 1. (Willard Exercise 19B.1) Show that the onepoint compactication of Rn is
homeomorphic to the ndimensional sphere S n .
Solution. Note that S n is compact, and a punctured sphere S n \c
Math 535  General Topology
Fall 2012
Homework 7 Solutions
Problem 1. Let X be a topological space and (Y, d) a metric space. A sequence (fn )nN of
functions fn : X Y converges uniformly to a function f : X Y if for all > 0, there is
an N N satisfying
for
Math 535  General Topology
Fall 2012
Homework 2 Solutions
Problem 1. (Brown Exercise 2.4.5) Consider X = [0, 2] \ cfw_1 as a subspace of the real line
R. Show that the subset [0, 1) X is both open and closed in X .
Solution. [0, 1) is open in X because w
Math 535  General Topology
Fall 2012
Homework 1 Solutions
Denition. Let V be a (real or complex) vector space. A norm on V is a function : V R
satisfying:
1. Positivity: x 0 for all x V and moreover x = 0 holds if and only if x = 0.
2. Homogeneity: x = 
Math 535  General Topology
Fall 2012
Homework 3 Solutions
Problem 1. Let S 1 R2 be unit circle in the plane, with the subspace topology. Consider
the winding map
f : R S1
t (cos t, sin t).
Show that f induces a homeomorphism R/ S 1 , where the equivalenc
Math 535  General Topology
Fall 2012
Homework 4 Solutions
Problem 1. Let cfw_ A be a family of directed set. Show that the product
becomes a directed set by dening the relation
A
if in for all A
i.e. the componentwise preorder. (First check that this is
Math 535  General Topology
Fall 2012
Homework 6 Solutions
Problem 1. Let F be the eld R or C of real or complex numbers. Let n 1 and denote by
F[x1 , x2 , . . . , xn ] the set of all polynomials in n variables with coecients in F.
A subset C Fn of ndime
'Mexico is one big cemetery': The search for the
secret graves of 'the disappeared'
InVeracruz,Mexico,volunteershavebeensearchingforclandestinegraves.
ByPatrickJ.McDonnell
SEPTEMBER29,2016,3:00AM
T

REPORTINGFROMVERACRUZ,MEXICO
heygathershortlyafterdaybr