Here's the latest on the PIF Race to the WTA Finals, along with a rankings update after an action-packed week across multiple events:

Race update

Entering this week, Iga Swiatek and Aryna Sabalenka are still the only two players who have qualified for the WTA Finals, leaving six spots open, to be decided in the final month of the season. With up to 3,500 points remaining up for grabs, the stage is set for an exciting final swing. 

Elena Rybakina, Jasmine Paolini and Jessica Pegula own a significant lead at the No.3, No.4 and No.5 spots on the leaderboard, holding a 1,200-plus point cushion over anyone outside the Top 7. 

Coco Gauff and Emma Navarro hold the No.6 and No.7 spots on the leaderboard.

For Barbora Krejcikova, scenarios for qualification for the WTA Finals looks slightly different. As a Grand Slam champion, the Wimbledon champion needs to secure a Top 20 leaderboard finish to punch her ticket to Riyadh. In its first year as a qualification rule for the WTA, the highest ranked Grand Slam champion ranked No.8-20 secures a spot. 

This week in Seoul, a WTA 500, Daria Kasatkina (No.13), Marta Kostyuk (No.15) and Diana Shnaider (No.16) are the highest positioned players in the draw. Although each can make significant gains, no one can move into the Top 7.

After this week, the tour calendar shifts to the final two WTA 1000 events of the year in Beijing and Wuhan, with nearly everyone on in contention entered to compete.

Rankings movements

Last week, several players made breakthroughs at the Guadalajara WTA 500 and Monastir WTA 250 events. Though there was no change in the Top 25, a number of players have made significant jumps on the PIF WTA Rankings.

Guadalajara champion Magdalena Frech enters the Top 40 for the first time after winning her first Hologic WTA Tour trophy. Frech  -- who reached the fourth round at the Australian Open and made her first final in Prague in July -- rises 11 places to No.32.

Neither Olivia Gadecki nor Sonay Kartal had reached a tour-level quarterfinal before last week, and they had to go through qualifying just to reach their main draws. But Gadecki made it to the Guadalajara final, upsetting Danielle Collins -- her second Top 20 win -- along the way, and Kartal claimed the Monastir title in just her seventh main-draw appearance.

Both players make their Top 100 debuts this week. Australia's Gadecki shoots up 64 places to No.88, and Great Britain's Kartal rises 55 spots to No.96. Kartal, who now owns a 44-7 overall record this season, was ranked as low as No.303 in June.

Guadalajara semifinalist Camila Osorio, who reached the last four of a WTA 500 event for the first time, climbs 19 places to No.61. Monastir runner-up Rebecca Sramkova is up 34 to No.102 after reaching her first WTA final.

Other players reaching new career highs this week include Guadalajara quarterfinalist Marina Stakusic  (+27 to No.128) and Monastir quarterfinalists Yuliia Starodubtseva (+12 to No.118) and Antonia Ruzic (+19 to No.154).

At the WTA 125 level, former No.21 Jil Teichmann took the Ljubljana title and climbs 37 places to No.145. In Bucharest, home hope Miriam Bulgaru lifted the trophy. She is up 24 places to a new career high of No.178.

Meanwhile, France's Tessah Andrianjafitrimo extended her winning streak to 10 matches after claiming the ITF W75 title in Le Neubourg and moves up 126 places to No.303.