Daydream

A Daydream is a dream that occurs during the day, which opens a gate to the world of dreams. The vast majority of Daydreams occur when a Dream Demon has found its vessel and is trying to obtain it. Acting as a closed space of sorts, Dream Demons are forcefully pulled into this world and are unable to escape. In some cases, Dream Demons can be pulled into these spaces by other Dream Demons. For the most part, only Dream Demons and their vessels are able to enter Daydreams, however, it is important to note that there are exceptions to this rule. Take Yumeji, for instance.

Each Dream Demon has its own unique dream world, and each world has a different look and feel.

John Doe's Dream World
In John Doe's daydream we see a lot of skeleton fish flying in one place. The entire world is a town that looks like a port or a western city. When Yumeji was in the daydream, we saw an army of cats attacking him. John Doe states that he created this daydream so only Yumeji and him can enter.

Engi Threepiece's Dream World
In Engi's daydream we see a field of some type of flower and the moon. When the moon is in the sky in her daydream, Engi can summon her swords over and over again. In her dream world there is a giant rock, that Yui hides in. When she pulls other Dream Demons to her daydream, Yui goes there and hides.

Chris Evergreen's Dream World
Chris's daydream is a church. It is dark and it has some plants with thorns there. There are also huge windows which Merry broke through in Episode 4. When Chris made Mei his vessel, she was seen sleeping in a bed full of flowers.

Clione's Dream World
The daydream of Clione is a great theater full of banks and in the middle is a big stage where Clione usually sings.

Merry's Dream World
The daydream of Merry is the door between the real world and dream world. If many nightmares cross through the door Merry weakens. If it were to be destroyed, Merry would die.

Properties
Dream Demon's coexist with their Dream World, so if either the Demon or the World is destroyed, the other will cease to exist. However, because of this coexistance, a Dream Demon's power is greater when they are within their own World, and have the option to flee from a fight within their own World at will if neccessary.

Dream Demons however are essentially trapped if they are pulled into another's World, and can only leave by the owner of the World dropping the World themselves. Therefore, if a Dream Demon is being attacked by another who has drawn them into their World, the only means of escape is by defeating them.