By Art Spander  

NEW YORK — Oh, the the things that took place after Sloane Stephens, the designated “heir apparent” to Serena Williams, beat a semi-injured Williams in the quarterfinals of the Australian Open in January.

Stephens, 19 at the time — she’s now 20 — once had a poster of Serena in her room but allowed, in one of those moments when elation blurs logic, “I think I’ll put a poster of myself now.”
    
Then a month or so later, Stephens bemoaned the fallout, saying Serena unfollowed her on Twitter and that in truth Serena had in “the first 16 years of my life never said one word to me.”
  
What Serena said to Sloane Sunday, after their fourth-round match in the U.S, Open ended with Williams, having won the final five games and verifying her status with a 6-4, 6-1 victory, was “Good job.”
   
What Stephens said was, “I mean, obviously, she’s No. 1 in the world for a reason.” Obviously.

Serena will be 32 at the end of September, ancient for an athlete in a sport where there always seems to be another teenage phenom coming along. From Serbia or Spain or Russia.
  
Which is why so much — too much? — was made of Serena and Sloane, two women who, if not actually the rivals some journalists choose to call them, at least both are Americans.
   
You know, mom, apple pie and forehands. Also, alluding to that match eight months ago, revenge.
    
There was a misplaced assumption that, perhaps because they both are African-American, Serena had become Stephens’ mentor, as well as her bosom buddy. But tennis players, as golfers, do not become friendly with the people they are trying to pummel until retirement.
   
Arnie and Jack were competitors. Pete and Andre were competitors. Serena and Sloane are competitors.
 
“I think it was a high-quality match,” said Williams, and it was until it wasn’t.
  
Stephens isn’t in Serena’s class yet. She hung in for a while, which is what happens so often, but Williams won the big points in the first set and then won most of the points. Stephens was beaten mentally as well as physically.
  
“The second set got away from me a little bit,” confirmed Stephens. “I thought she did a lot of things well.”
   
Women’s tennis is dominated by very few, mainly Serena, Victoria Azarenka and Agnieszka Radwanska, and Radwanska has never won a Grand Slam tournament. Stephens is 15th in the rankings. “But I have a chance to break the top 10 at the end of the year,” she said.

She didn’t have much of a chance against Serena, even though it was 4-4 in the first set. The crowd, which didn’t quite fill 23,000-seat Arthur Ashe Stadium, seemed to favor Williams if marginally at the start. What it wanted most was a close match, and for about 45 minutes that’s what it got. Then, wham.

“I think she had some bomb first serves,” Stephens said of Williams, who broke her in the fourth game of the second set. “I lose serve. That kind of threw me off. I think having Serena serve up 3-1 is not ideal. When you give her that opportunity, to take that step forward, she definitely takes it.”
   
Williams has won the Open four times and, with the win over Stephens, advanced to the quarters 11 times in 14 appearances. Overall, of course, she has 16 Grand Slam titles, the most recent at the French Open in the beginning of June.
  
“I just tried to do what I wanted to do,” said Williams. If that was confusing, her game was not. She pounded serves, chased down balls on the lines and never reduced the pressure.
  
“Maybe one day when she’s not playing,” said a hopeful Stephens when asked about being on the same side of the draw as Serena, “people maybe would say, ‘I wish I wasn’t on the same side as Sloane.’
  
“Things happen in their time. It’s an honor to play on the court with one of the greatest tennis players of all time.”
  
That player was relentless.
  
“I’ve been at this a long time,” answered Serena about a possible letdown in her next match, against Carla Suarez Navarro of Spain. “So for me, in my career, there are no letdowns.
   
“I don’t go out there thinking about being a star. I just want to play tennis, and I want to do really good at it. It’s not about the stage for me. It’s just about getting the ball in.”
  
She got it in against Sloane Stephens as much as needed.