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Topological concepts similar to continuity. (English. Russian original) Zbl 0636.54040

Sib. Math. J. 28, No. 1-2, 113-119 (1987); translation from Sib. Mat. Zh. 28, No. 1(161), 149-156 (1987).
The article contains a description of \(\forall \exists\)-monadic construction via net and subsets related to corresponding filters. Applications to compact filters \((=filters\) with monads in nearstandard parts of the sets under consideration) are given.
Reviewer: S.S.Kutateladze

MSC:

54J05 Nonstandard topology
03H99 Nonstandard models
54C05 Continuous maps
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References:

[1] Sz. Dolecki, ?Tangency and differentiation: some applications of convergence theory,? Ann. Mat. Pura Applic.,130, 223-255 (1982). · Zbl 0518.49009 · doi:10.1007/BF01761497
[2] J.-P. Penot, ?Compact nets, filters and relations,? J. Math. Anal. Appl.,93, No. 2, 400-417 (1983). · Zbl 0537.54002 · doi:10.1016/0022-247X(83)90184-1
[3] R. V. Fuller, ?Relations among continuous and various non-continuous functions,? Pac. J. Math.,25, No. 3, 495-509 (1968). · Zbl 0165.25304
[4] R. E. Smithson, ?Subcontinuity for multifunctions,? Pac. J. Math.,61, No. 4, 283-288 (1975). · Zbl 0317.54022
[5] W. A. J. Luxemburg, ?A general theory of monads,? in: Applications of Model Theory to Algebra, Analysis and Probability, Holt, Rinehart and Winston, New York (1969), pp. 18-86. · Zbl 0207.52402
[6] K. D. Stroyan and W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Academic Press, New York (1976).
[7] J. F. Aarnes and P. R. Andenaes, ?On nets and filters,? Math. Scand.,31, No. 2, 285-292 (1972).
[8] K. Kuratowsky, Topology, Vol. 1, Academic Press (1966).
[9] S. S. Kutateladze, ?Infinitesimal tangent cones,? Sib. Mat. Zh.,26, No. 6, 67-76 (1985).
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