At the end of the 19th century and the beginning of the 20th, parasols were common in photos. They were the fashion accessory of the time and for good reason; women's complexions were to be pale, not tanned. Pale skin showed you were upperclass, tanned scan was for the working class.
I'd love to be able to collect antique parasols, but rarely see them. They often look to be Asian, but perhaps there were companies in the US manufacturing them to look Asian. I haven't a clue. I do know that they are a category, a vernacular photography category.
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Visit this site to see some lovely impressionist paintings of women with parasols by American artist Frederick Frieseke.