Reb Eliezer: proud, look up in Biur Halacha O’CH 554 about the Cholara epidemic to stay inside but when need to go out, wear a mask.
No, he does not say that. Please do not repeat things that you saw quoted somewhere but did not bother looking up yourself. If you had looked it up you would have seen that the person who quoted it to you was lying or incompetent.
The Biur Halacha says that if someone insists on fasting during a cholera epidemic, then he should protect himself by staying home to avoid breathing the bad air that was then falsely thought to cause the disease. If he must go out, he should hang some camphor and mint leaves over his nose, in the hope that the strong smell will protect him from the bad air. NOTHING about masks. Anyone who tells you he mentions a mask is not telling you the truth.
Of course nowadays we know that cholera has nothing to do with bad air, and all the precautions people thought they were taking were useless. They should have been doing something very different: boiling and/or chlorinating their water, and washing their hands frequently (in clean water!) Which goes to show that the so-called “experts” don’t necessarily know what they’re talking about. And that applies now just as it did then.