Ascoli's thoerems

• Autorzy: Pasicki L.
• Języki publikacji: EN

Abstrakty

EN

We present some elegant and pretty general versions of Ascoli theorem for non-Hausdorff spaces. The proofs are simple and elementary (e.g. we do not use the notion of joint continuity) while the results seem to be a very good starting point for more sophisticated theorems. Due to Lemma 10 (it extends [1], Th. 2.2) each of our theorems concerning even continuity is sufficiently general to contain the respective "equicontinuous" one (see Remark 18). Kelley in [2] (as regards the Ascoli theorems) was oriented mainly on continuous mappings while the present paper shows that it is natural first to get "continuous on compacta" results and t hen the "continuous1' versions become their simple consequences.

Słowa kluczowe

EN

Ascoli theorem; even continuity

PL

twierdzenie Ascolego; ciągła parzysta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 2
• Strony: 429--434
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Pasicki L.

• Faculty of Applied Mathematics AGH University of Science and Technology Al. Mickiewicza 30 30-059 Kraków, Poland,

Bibliografia

• [1] G. Fox, P. Morales, A non-Hausdorff Ascoli theorem for k3-spaces, Proc. Amer. Math. Soc. 39 (1973), 633-636.
• [2] J. L. Kelley, General Topology, Springer, New York Heidelberg Berlin, 1975.
• [3] N. Noble, The continuity of function on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198.