Let . What is the maximum order can have?

# Month: July 2016

# No point left behind

Every infinite set admits a metric with no isolated points.

# Walk like an Egyptian

Let be a fixed positive integer and let be distinct positive integers such that

Find the maximum possible value ofÂ .

# Dense totients

Show that the set of numbers of the form is dense in the closed unit interval.

# Keeping it real

Let be a matrix with a real, simple eigenvalue. Prove that there exists a neighborhood of in which all matrices have at least one real eigenvalue.

# Compact function spaces

Let be a compact metric space, a continuous function and . Prove that is compact iff is finite.