NEW YORK— Rudolph Giuliani, the former mayor of New York City, is in critical but stable condition at a hospital, his spokesman said Sunday. Spokesman Ted Goodman didn’t say what sent the 81-year-old to the hospital or how long he’s been there. “Mayor Giuliani is a fighter who has faced every challenge in his life with unwavering strength, and he’s fighting with that same level of strength as we speak,” Goodman said in a statement on social media. He said Giuliani “remains in critical but stable condition.” Giuliani hosted his online show, “America’s Mayor Live,” Friday night from Palm Beach, Florida. As he opened the show, he coughed and his voice sounded more raspy than usual. He remarked: “My voice is a little under the weather, so I won’t be able to speak as loudly as I usually do, but I’ll get closer to the microphone.” Giuliani earned the “America’s Mayor” nickname for helping unite the nation following the Sept. 11 attacks.…