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The Quarterly Journal of Mathematics 2000 51(3):299-306; doi:10.1093/qjmath/51.3.299
© 2000 by Oxford University Press
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Interiority of real functions

JANUSZ J. CHARATONIK1,*, KRZYSZTOF OMILJANOWSKI1,§, Alfonso Villani2 and §,¶

1 Mathematical Institute, University of Wroclaw pl., Grunwaldzki 2/4, 50-384, Wrocl aw, Poland 2 Department of Mathematics, University of Catania, viale A. Doria, 6, 95125 Catania, Italy

Conditions concerning openness of continuous real functions defined on topological spaces are studied. It is shown that for locally compact metrizable spaces interiority of the function at a point is equivalent to having no local extremum at this point if and only if the domain space is connected im kleinen at the point. Some related results are some obtained and open questions are posed.

Received 12 May, 1998. Revised 3 September, 1998.

* E-mail: hmsri@uvvm.uvic.ca

§ E-mail: vu@math-1.sci.kuniv.edu.kw

Present address: Departamento de Matemática Pura, Facultade de Ciencias, Universidade de Porto, P-4099-002 Porto, Portugal. E-mail: S.Yakubovich@agc0.fc.up.pt


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