Meadowhall has warned shoppers that many retailers, including some department stores, have decided to close due to the extreme weather conditions.
The shopping centre has advised customers to contact stores before heading out to check whether they are open.
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House of Fraser announced at around 4pm today that it was closing early due to what it called the 'inclement' weather.
It advised customers: "We hope to be back and up running soon, but in the meantime check out the House of Fraser site for all your cold weather buys."
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An automated message on the Debenhams phone line, meanwhile, said: "Due to the extreme weather conditions, we have closed early to allow our staff to get home safely. We will reopen as normal tomorrow morning."
Becky Kituyi welcomed the decision by some shops to close early, saying: "Good! Safety over profit! Hope all staff and visitors get home safely."