Urysohn's lemma
Not what you're looking for?
A Hausdorff space is said to be completely regular if
for each pt. x in X and closed set C with x not in C,
there exists a continuous function f: X --> {0,1} s.t.
f(x)=0 and f(C)={1}.
Show that if a space is normal, it is completely regular.
How do I use Urysohn's lemma along with Hausdorffiness to show this.
Thank You
Purchase this Solution
Solution Summary
This is a proof regarding regular and normal spaces. The expert examines Hausdorffiness lemmas.
Solution Preview
Urysohn's Lemma: The topological space X satisfies T4 axiom if and only if for any nonintersected closed set A and B, there exists a continuous function f: X->[0,1], such that f(A)={0}, ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.