no, but she did want to marry someone to be king of ithika and to be a daddy to telemakos
hope this help
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Odysseus returns home to his wife Penelope and their son after being away fighting and being shipwrecked to find a host of suitors all wanting to marry Penelope.So Odysseus dressed as a beggar and hung around the suitors so that he could see if anything untoward was taking place with anyone of them and Penelope,which of course there wasn't so Odysseus killed all of the suitors before declaring his presence to Penelope.
Odysseus accuses Penelope of being hardhearted because she has remained faithful to him for 20 years, delaying the suitors who are trying to marry her while he is away. In his disguise as a beggar, Odysseus tests Penelope's loyalty before revealing his true identity.
Penelope is the wife of Odysseus, when Odysseus was away she was purseued by many suitors. She said she would only marry them when she had finished the tapestry she was making, she continued to work on the tapestry but unpicked her work each night. When Odysseus finally returned home her through out all the suitors. Penelope is offered as the epitome of a faithful wife. She had every reason to believe Odysseus was dead, and no one would have faulted her for taking another husband. But she remained faithful to her husband nonetheless. This
Odysseus instructs Penelope to wait for him and to guard their home in his absence. He also warns her not to remarry and assures her that he will return to her soon.
In The Odyssey, going home was Odysseus' ultimate goal. He had been away at war for years, and he desperately missed his wife, Penelope. Odysseus knew Penelope may have believed him to be dead, so he needed to get back to her.
Odysseus had been many years - some say as many as ten, or more - away from Penelope - their son had grown up, but his life had aged him, as well that he went in disguise.
Odysseus told Penelope to make sure the suitors did not gain control of their household, to stay faithful to him, and to keep their son Telemachus safe.
Penelope believes that the beggar is her husband, Odysseus, who has returned home in disguise after being away for many years. She tests him by asking him to move their bed, a task only Odysseus could accomplish due to its special construction.
Eurymachus is one of the suitors vying for Penelope's hand in marriage while Odysseus is away. He is shown as a manipulative and deceitful character, trying to gain favor with Penelope and plotting against Odysseus. Eurymachus is part of the group that takes advantage of Odysseus's absence by feasting and trying to win over Penelope.
Penelope's main conflict in "The Odyssey" is dealing with the suitors who are trying to marry her while her husband Odysseus is away. She must balance her loyalty to Odysseus with the pressure to choose a suitor. This conflict drives much of the tension in the epic as Penelope tries to outwit the suitors and remain faithful to her husband.
Penelope's ostensible offer of marriage and her solicitation of gifts constitute a dolos with a double aim: to keep the suitors off guard and to reassure Odysseus of her loyalty, in the well-founded belief that he has today returned in the guise of the stranger.
While Odysseus is away from Ithaca, several of the lords and chiefs are heading over to where Odysseus has built his home because they believe that their King is dead. The begin to try and get Penelope to marry them and anger Telemachus who believes that his father is still alive. Athena eventually comes and tells Telemachus that his father is in fact still alive and then tells him what he must do to get the suitors to leave.