The word "public" refers to something that is shared or accessible by everyone in a community, rather than being private or exclusive to certain individuals. Full definition
I think that all the time when I read school food success reform stories for small schools, private schools, charter schools in public school districts. (thelunchtray.com)
Parents must pay taxes in support of public schools as well as tuition for private ones. (religion-online.org)
Why have churches been meeting in public schools for decades without anyone bringing suit? (religion.blogs.cnn.com)