The section of the short story you want to look at is the second paragraph, which gives us an excellent description of the setting of this story and also reveals how this reflects Prince Prospero's character. Consider the way in which Prince Prospero's response to the Red Death is to retire to the "deep seclusion of one of his castellated abbeys." Note the way that this abbey is described with particular emphasis placed on its impenetrability:
A strong and lofty wall girdled it in. This wall had gates of iron. The courtiers, having entered, brought furnaces and massy hammers and welded the bolts. They resolved to leave means neither of ingress or egress to the sudden impulses of despair or of frenzy from within.
Quite clearly, the Prince and his friends hope to cheat death by locking themselves away from the world and continuing their hedonistic way of life. Prince Prospero's arrogance and bravery in trying to cheat death is thus shown, as is his selfishness and his lack of care and concern for those left on the outside.