Yes, there are folding bikes. Brompton and Dahon are two makers.

Leisure Lakes Bikes sell a huge range of bikes. They sell mountain bikes, road bikes, folding bikes, BMX bikes, Hybrid bikes, electric bikes and kids bikes.

Researching Korean bicycle manufacturers has found that one company called Samchuly is the largest manufacturer of bikes in Korea. The company makes a large variety of bikes such as folding bikes, racing bikes, children's bikes, women's bikes and mountain bikes.

The Dahon folding bikes are advertised as being 'the worlds best selling folding bike'. There are over 20 different models available. Each model features a strong, light-weight frame that can be quickly folded up for easy storage/transportation.

They are good if you want to store them easily.