E MA We define the included point topology by Tp%3{ UcR;U=Ø or pEU). Let A = [3,5[, then A is dense in R if * O Ris equipped with Tp and p 5 Ris equipped with the usual topology Ris equipped with Tp...

Extracted text: E MA We define the included point topology by Tp%3{ UcR;U=Ø or pEU). Let A = [3,5[, then A is dense in R if * O Ris equipped with Tp and p 5 Ris equipped with the usual topology Ris equipped with Tp and p -4 O None of the choices A property is said to be a topological property if it is preserved by homeomorphism. Suppose that Ris equipped with the usual topology. then the boundedness and the closedness are not topological properties because


Extracted text: ces A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because Ris homeomorphic to ]0,1[ O Ris homeomorphic to J0, +o[ O -0] is homeomorphic to [0,+ O [0,1) is not homeomorphic to ]0,1[ Let X be an infinite set with the finite closed topology T-(S subset of X; X-S is finite). Then