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She has been ranked by the Women's Tennis Association (WTA) as high as world No. 31 in singles and No. 81 in doubles. She has won two singles titles and one doubles title on the WTA Tour plus one doubles title at WTA 125 tournaments, along with six singles and five doubles titles on the ITF Circuit.
A former junior world No. 3, Teichmann won a Grand Slam title in the girls' doubles event at the 2014 US Open. That year, she also won a gold medal for Switzerland in mixed doubles at the Summer Youth Olympics in Nanjing.
Her breakthrough as a senior player came in May 2019 when she won her first WTA title in Prague. In July of that year, she won another WTA tournament title after making her first top-10 win over Kiki Bertens. She continued progressing, in March 2021 reaching the semifinals of the WTA 1000 Dubai Championships. With these performances she entered the top 50. Later that year, she reached the final of the Cincinnati Open, a WTA 1000 event, defeating Naomi Osaka, Belinda Bencic, and Karolína Plíšková, before falling to world No. 1, Ashleigh Barty.

Teichmann at the 2019 Open de Limoges

