MASOUMEH NAJAFI TAVANI

We first show that in a topological Q-algebra, the spectrum function is upper semicontinuous and hence the spectral radius function is upper semicontinuous. Then we prove that each homomorphism from a topological Q-algebra onto an advertibly complete semisimple lmc algebra has a closed graph. Consequently, if A is a complete metrizable Q-algebra and B is a semisimple Fr´echet algebra, then every surjective homomorphism T : A→ B is automatically continuous.

Topological algebra, Q-algebra, spectrum function, upper semicontinuity, automatic continuity