Applied Categorical Structures

, Volume 22, Issue 3, pp 551–563

Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity

  • Eva Colebunders
  • Frédéric Mynard
  • William Trott

DOI: 10.1007/s10485-013-9321-z

Cite this article as:
Colebunders, E., Mynard, F. & Trott, W. Appl Categor Struct (2014) 22: 551. doi:10.1007/s10485-013-9321-z


Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to convergence-approach spaces. Characterizations are obtained for two alternative extensions of regularity to convergence-approach spaces: regularity and strong regularity. The results improve upon what is known even in the convergence case. On the way, a new notion of strictness for convergence-approach spaces is introduced.


RegularityStrong regularityConvergence spaceConvergence-approach spaceApproach spaceStrict subspaceContinuous extensionContractive extensionDefault of contractionContinuous convergenceDiagonal axioms

Mathematics Subject Classifications (2010)


Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Eva Colebunders
    • 1
  • Frédéric Mynard
    • 2
  • William Trott
    • 2
  1. 1.Vakgroep WiskundeVrije Universiteit BrusselBrusselBelgië
  2. 2.Mathematical SciencesGeorgia Southern UniversityStatesboroUSA