The book by Hindman&Strauss has a section on filters and compactifications in a later chapter — that might be suitable for 2).

]]>Possibly relevant is my October 2004 sci.math post “Generalized Quantifiers” (URLs below). FYI, the Math Forum version has a lot of strange formatting errors. See also Brian Thomson’s 1985 book “Real Functions”, and see Thomson’s earlier 2-part survey Derivation bases on the real line (which contain examples and side-detours not in his book).

google sci.math URL:

https://groups.google.com/forum/#!msg/sci.math/rhZEhXynVLQ/MI0MJ0ZQIvoJ

Math Forum sci.math URL:

http://mathforum.org/kb/message.jspa?messageID=3556191