Course Code
mth402


Question
If \(\tau\) is a topology on X, which of these is trueabout \(\tau\)?

Answer
Finite intersctions of elements of \(\tau\) are in \(\tau\)



Question
The countable collection B = { ( a, b ) : a

Answer
Basis



Question
Let X be a topological space. Then one of the following conditions does not hold

Answer
Infinite unions of closed sets are closed



Question
Let \(\pi_{1}( x, y) =x\) and \(\pi_{2}( x,y) =y \)then \(\pi_{1} : X x Y\rightarrow X \)and \(\pi_{2} : X x X\rightarrow\) Y. The maps \(\pi_{1}\) and \(\pi_{2}\) are called ____________________________

Answer
Projections of X x X



Question
A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that

Answer
B_d( x,\(\epsilon)\subset\bigcup\)



Question
A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following:

Answer
\(d(x,y) = 0 \)whenever \(\neq\) and \(x,y\epsilon X\)



Question
Let \(\mathbb R\) be with the usual standard topology and let A \subsets\mathbb R\).Then A is open in \(\mathbb R\) if there exists an interval I such that I\subset A. For a,b\(\epsilon\mathbb R, I =

Answer
I = ( a, b)



Question
\(B\)' is the lower limit topology on \(\mathbb R\) if

Answer
\(\mathbb B' = {[a,b) : a,b\epsilon\mathbb R; a 


Question
When is \(B\) aneuclidean topology \(\mathbb R?\) When

Answer
\(\mathbb B = (a,b): a,b\epsilon\mathbb R, a 


Question
Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold:

Answer
The set X x X is also a member of \(\chi\)


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