# left uniform continuous function that is not right uniform continuous

Consider the following problem 5 below.

I am trying to construct the stated function f. I tried many functions one which sends the matrix of the form below to xy. I also tried to send the matrices of the form below to x + y. None of them work.

Recall a left uniform continuous function f on G is defined as follows. First define the left and right translated of f through y by:

$$L_yf(x) = f(y^{-1}x)$$ $$R_yf(x) = f(xy)$$

f is called left (resp. right) uniformly continuous if for every $$\epsilon$$ there is a neighborhood V of e such that $$\|L_yf - f\|_u < \epsilon$$ resp $$\|R_yf - f\|_u < \epsilon$$ for $$y \in V$$. We are working with uniform continuity here. Does anyone the correct function here ?

• Could you define what is meant by "left/right uniformly continuous function on G" ? – elidiot Apr 23 '19 at 17:20
• I have edited the question. – user329017 Apr 23 '19 at 17:36