How is heroism portrayed in The Odyssey?

In The Odyssey, heroism is portrayed as something which men are capable of -- Penelope is cunning and clever, but she is never discussed as heroic -- and heroism is achievable by fighting external enemies (like monsters), overcoming physical challenges (like going to the Underworld) with bravery, and exhibiting good character.  Odysseus does all these things.  He goes up against monsters like Scylla and Charybdis and Polyphemus, but he also exhibits good character qualities...

In The Odyssey, heroism is portrayed as something which men are capable of -- Penelope is cunning and clever, but she is never discussed as heroic -- and heroism is achievable by fighting external enemies (like monsters), overcoming physical challenges (like going to the Underworld) with bravery, and exhibiting good character.  Odysseus does all these things.  He goes up against monsters like Scylla and Charybdis and Polyphemus, but he also exhibits good character qualities when he refuses to hide below deck, for example, when his ship must pass Scylla.  He knows that she will likely eat six of his men, and he casts his lot with the rest of them, standing on deck and brandishing his sword against her.  Further, when he goes to blind Polyphemus so that he and his men can make their escape, he takes it upon himself to lead the most dangerous part of that mission: actually stabbing the Cyclops in the eye.  Heroism is thus presented as something that a man can achieve by taking on the evil or the monstrous as well as by putting the needs of others before his own.