No man is an island, but some men own one.

Bjorn Borg, who at age 23 is earning approximately $3 million a year as the best tennis player in the world, owns a group of 11 islands in the Baltic Sea, off the east coast of his native Sweden, in a maritime region known as Gryt.

The main island is Kattilo, pronounced "Shat-a-leu." To get there, Borg says, you drive four hours north from Stockholm, along the coast toward Goteborg, and then take a launch. "It takes 15-20 minutes with a fast boat, to get out there."

Borg smiled fondly today after his third-round victory over Jaime Fillol in the U.S. Open as he described his hideway paradise, so far from the heat and noise of Flushing Meadow Park, where he is favored to win the third leg of a possible Grand Slam next weekend.

It's a big island, with a lot of houses on it for guests, but there are only two families living there," he said.

"We live on one side of the island, and another family on the other side. My parents are living there in the summer, and the rest of the year they spend in Monte Carlo.

I don't know how many hectares, but it is a lot of land, a lot of area. My house is near the water. You can swim right there, the water is fine. There's a bit of farmland on the other side. The other family has cows, sheep, these kind of things. They live there all year, and look after it when I'm away."

On the tennis circuit, Borg lives unpretentiously. His favorite clothes are T-shirts and jeans. Getting dressed up means putting on a warmup suit. In the era of the blow-dry athlete, he lets his scraggly blond hair dry naturally in the sunshine. His stubbly beard is happily unkempt.

He likes watching television, reading magazines and comic books, and eating leisurely, room-service meals with his fiancee, Romanian player Marianna Simionescu, and Lennart Bergelin, his longtime friend-coach-trainer-confidant. Borg, whose normal pulse rate is an astonishingly low 35, has refined doing nothing-- just relaxing" to a fine art.

Away from the globetrotting life of the tennis tour, he has similarly simple tastes, but relaxes in style. He owns a house and an apartment in Monte Carlo, the tax haven that is his official residence. His parents-- Margaretha and Rune Borg, who was a clothing salesman when he won a tennis racket as a prize in a table tennis tournament and gave it to his only child, then 9 years old-- have an apartment there and operate a sporting goods shop that Bjorn bought for them.

And there is Kattilo, which Borg refers to simply as "my island."

It was there, two weeks after he won his fourth consecutive Wimbledon singles title in July, that Borg began preparing for the U.S. Open . . . by virtually putting his racket away for two weeks.

He was exhausted, more mentally than physically, after a long siege of tennis. In june, he won the French Open, the world's premier clay-court tournament, for the fourth time. Then his fourth straight Wimbledon, a feat last achieved by New Zealander Tony Wilding in 1910-13. Then he went to Bucharest and won both his singles as Sweden beat Romania in a Davis Cup series, and to Baastad, where he won the Swedish Open.

"Too many matches. He was really tired. He had to stop," Bergelin said. Borg has not lost a match since he had to default from the German Open in May with a pulled groin muscle, and his 6-0, 6-3, 6-1 romp over Filiol today stretched his current winning streak to 30.

But in July, he was drained. He needed a little R&R. He went to Katilo with Simionescu and an old friend from the school in Sodertalje, a Stockholm suburb, that he left at age 15 to pursue a career in tennis.

"I had three weeks off, and for 2-1/2 weeks I didn't touch a racket. I was just enjoying myself. I didn't think about tennis, didn't think about U.S. Open, just relaxed as much as I could," said Borg, who inwardly sometimes resents the image so many people have of him as an emotionless tennis machine who never runs down and all but operates on automatic pilot.

"I need this time, a holiday when I just do anything except playing tennis. You know, like staying up every single night."

"You really howl, eh?" inquired a young woman.

"Yah," Borg grinned with engaging sheepishness. "That's right."

On Kattilo, Borg swam and took parties of friends out on the fishing boat that the previous owner sold him along with the island and all its buildings. He raced his other boat-- "a little Flipper, they call it," said Bergelin, "catamaran style. Very small, but fast. A nice racing boat for five persons." He spent time with his parents.

"This is very important for him sometimes-- you know, living a family life," said Bergelin, 53, the rawboned former Swedish Davis Cup player and captain who has been Borg's mentor and companion since he was 12, and remains his shield against an intruding world at tournaments.

"He sees his parents so seldom, of course there is much to talk about. And he has a lot of Swedish friends he does not see so often. He catches up on the whole year in a few weeks.

"When he has a holiday like this, he really has to slow down all the way, so he really feels he has no pressure on him," Bergelin went on. "It's very important that the first 10, 14 days, he more or less doesn't touch a racket. Maybe he plays one hour sometimes with Mariana, just to feel the ball a little bit. But no pressure at all."

Three days before the end of the vacation, Bergelin went to Kattilo to begin practicing with Borg. Billy Martin, a young American and frequent practice partner who had been playing in a tournament an hour away, came along to spar. Then Borg went to Toronto to play the Canadian Open on hard courts similar to the rubberized asphalt ones on which the U.S. Open is played at the new National Tennis Center.

"I started to practice four, five hours a day. I was working really, hard," said Borg. "It was very hard in the beginning to get back into good shape again, after not playing and enjoying myself so much and not thinking about tennis. The first five, six days, I was playing terrible. But then I started to get back into good shape."

This is not an accident. Borg is one of the hardest, most tireless workers in tennis. His colleagues agree that there is no one fitter or more serious about practice. Vitas Gerulaitis-- another regular sparring partner at whose home in nearby Kings Point, L.I., Borg practiced the week before the Open-- usually plays disco music on the court, but he turns it off when Borg comes. It is all business.

"I could hardly believe his regimen," said Herbert Warren Wind, the distinguished writer for The New Yorker who has studied most of the best players in tennis for four decades, after observing Borg in Toronto. "He works harder than Rod Laver, than Roy Emerson, than any other player I've ever seen."

Borg long considered American hard courts-- cement, asphalt and similar surfaces-- to be foreign and uncomfortable. But he has learned to play on the Wimbledon grass to which many experts once predicted that he would be unable to adapt.

He won in Toronto. In the final, he routed John McEnroe-- the only man with an even record against Borg in the last year, having split six matches with him. This was Borg's second victory this year on hard courts. The last time he played on them, he won the Alan King Classic in Las Vegas in May, yielding only five games in the final to Jimmy Connors, the archrival to whom he has not lost a set in five meetings this year.

"I just know that I feel very confident now, much more comfortable on this surface than last year," Borg said. "Before, I was never winning on cement. Las Vegas was the first time. But now I am more used to it . . . I think if I can stay in good shape, no injuries, I have a good chance to win."

In the euphoria of his tense, five-set victory over Roscoe Tanner in this year's Wimbledon final, Borg revealed a little bit more of himself than he normally does.

"One of my goals in the future is to win maybe a lot of big titles and to make some records if I can, and maybe one day they will say, 'You have been the greatest player of all time,'" he said. "That is my ambition in the future . . .

"I think it is very difficult to improve more. Little things, maybe, especially my serve and my volley, but my ambition now is to stay at the same level the next five or six years, or how many years I play tennis, and keep winning big titles."

The fourth Wimbledon was his primary goal for 1979, but with that accomplished he is hungry to win his first U.S. Open. He has been in the final twice, losing to Connors in 1976 and 1978. Last year, he was hampered by a blister on his right thumb in the final. In 1977, he defaulted to Dick Stockton-- his next opponent here-- because of a shoulder injury suffered water skiing.

"I've been a little bit unlucky in this tournament, but I am not superstitious about it," Borg said. "Right now, I feel very good, very strong . . . For sure, nothing will happen this year. No injuries. I don't think so." He tapped the table top in front of him, knocking on wood for luck.

Meanwhile he is not taking any chances. No water skiing this year. He tapes his fingers before every match and practice session to prevent blisters. He has had the grips of his rackets reworked to make them softer. Bergelin fiddles with them with his pen knife, to make sure they do not rub the ball of Borg's palm, which is susceptible because of the looping, exaggerated topspin stroke with which he hits his forehand.

Borg has half a dozen pairs of tennis shoes to get him through the Open. He changes them frequently, another precaution against blisters that could result from a long match on broiling hard courts.

Bergelin overlooks no detail for his man.

He has three dozen rackets for Borg, strung at an incredible 80 pounds tension. Sometimes Borg's rackets are strung as tight as 90 pounds, but they are a little looser here because of the atmospheric conditions and heavy ball. Still, 80 pounds is not exactly loose. Most pro players have their rackets strung at between 60 and 70 pounds.

Borg needs specially made, heavy frames to support the tension. He has his own stringer in New York, too. Bergelin is a hard man to please when it comes to stringing rackets. At the French Open this year-- where Borg went through two dozen frames and 50 string jobs in two weeks-- Bergelin arranged a deal with Scandinavian Airlines, with whom Borg has an endorsement contract, to shuttle the rackets to Stockholm for restringing.

Borg says it takes luck to win a major tournament. He points to his narrow escapes from perilous positions at Wimbledon against Mark Edmondson in 1977, Victor Amaya in 1978, Vijay Amritraj this year.

"Usually, those matches come in the early rounds, before you get used to the courts, the balls, the conditions, before you find your own rhythm," Borg said. "I think always in a big tournament there is a match like that, when you don't play well. To survive a match like this, you must be lucky, because the difference is maybe one or two points.