Central Sets Theorem Near of an Idempotent in Wap-Compactification

A small part of real line which is very close to zero has rich combinatorial properties. The aim of this paper is to express and then prove some locally combinatorial concepts near a virtual idempotent by considering the wap-compactification of a semitopological semigroup S. The wap-compactification of a semitopological semigroup S, denoted by S-w, is the collection of all ultrafilters near eta is an element of S-w that forms a compact subsemigroup of beta S-d, where S-d denotes S as discrete space.