Vol. 29, No. 2, 1969

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Compactness of mappings

Edwin Duda

Vol. 29 (1969), No. 2, 259–266

A class of spaces that admit to a special kind of mapping onto the nonnegative real numbers is considered and it is shown that this particular type of space is invariant under compact monotone mappings. It is also shown that if such a space admits to a one to one (monotone) mapping onto a “nice” subset of the plane then the mapping is a homeomorphism (compact monotone mapping). If the one to one mapping (monotone) is not a homeomorphism (compact monotone mapping) then its range necessarily separates E2.

Mathematical Subject Classification
Primary: 54.60
Received: 6 August 1968
Published: 1 May 1969
Edwin Duda