Nikiel's conjecture

In mathematics, Nikiel's conjecture in general topology was a conjectural characterization of the continuous image of a compact total order. The conjecture was first formulated by {{ill|Jacek Nikiel|pl|Jacek Nikiel}} in 1986.{{cite journal

| first1=J. | last1=Nikiel

| title=Some problems on continuous images of compact ordered spaces

| journal=Questions and Answers in General Topology

| volume=4

| year=1986

| pages=117–128}} The conjecture was proven by Mary Ellen Rudin in 1999.{{cite journal

| first1=M.E. | last1=Rudin | authorlink1=Mary Ellen Rudin

| title=Nikiel's Conjecture

| journal=Topology and Its Applications

| volume=116

| year=2001

| issue=3 | pages=305–331

| doi=10.1016/S0166-8641(01)00218-8 | doi-access=free}}

The conjecture states that a compact topological space is the continuous image of a total order if and only if it is a monotonically normal space.