×

A note of decompositions of real line. (English) Zbl 0799.54008

Summary: For an arbitrary continuous bijection \(h\) of the real line onto itself there exists no homogeneous subgroup \(A\) of \(R\) such that \(A \cup h(A) = R\) is a decomposition into two disjoint parts.

MSC:

54B15 Quotient spaces, decompositions in general topology
54H15 Transformation groups and semigroups (topological aspects)
PDFBibTeX XMLCite
Full Text: EuDML