They didn't want to raise any false hopes , but they believed her husband had escaped capture.

他们并不想让人心存奢望，但是他们相信她的丈夫已逃脱追捕。

《牛津词典》

Do not allow yourself to indulge in false hopes.

不要让自己沉湎于虚无缥缈的期望之中。

youdao

Don't allow yourselves to indulge in false hopes.

不要让自己存有不切实际的希望。

youdao

He said it would create false hopes among former slaves.

VOA: special.2010.01.21

"Some have suggested in this campaign that Barack is guilty of raising 'false hopes, '" Kerry told a cheering crowd.

NPR: John Kerry Rallies with Obama in South Carolina

Part of his job is to represent the alliance to the world: encouraging would-be members, without giving them false hopes.

ECONOMIST: George Robertson, the new man for NATO

Jeff Bishop, from the Localism Network, said he thought the limitation of the bill could mean some communities entertained false hopes.

BBC: Bristol's Redcliffe Way could close under Localism Bill