Locally ordered topological spaces

• Autorzy: Pikul Piotr

Identyfikatory

DOI

10.4467/20842589RM.20.006.12438

• Języki publikacji: EN

Abstrakty

EN

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and separation axioms and give characterisation of those regularly locally ordered spaces which are connected, locally connected or Lindel¨of. We prove that local orderability is hereditary on open, connected or compact subsets. A collection of interesting examples is also offered.

Słowa kluczowe

EN

order topology; linear order; separation axioms; connected space; local connectedness; compact space; Lindel¨of space; hereditary property

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2020
• Tom: Vol. 55
• Strony: 113--141
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Pikul Piotr

• Instytut Matematyki, Wydzia l Matematyki i Informatyki Uniwersytet Jagiello´nski ul. Lojasiewicza 6, 30-348 Kraków, Poland

Bibliografia

• [1] H. Bennett, D. Lutzer, Recent Developments in the Topology of Ordered Spaces. In: Recent progress in general topology, II, North-Holland, Amsterdam, 2002, pp. 83–114.
• [2] R. Engelking, General Topology. Revised and completed edition. Heldermann Verlag, Berlin 1989.
• [3] H. Herrlich, Ordnungsf¨ahigkeit topologischer R¨aume. Dissertation, Berlin 1962.
• [4] M.S. Kurili´c, A. Pavlovi´c, Topologies given by closed intervals. Novi Sad J. Math. 35:1 (2005), 187–195.
• [5] D.J. Lutzer, A metrization theorem for linearly ordered spaces. Proc. Amer. Math. Soc. 22 (1969), 557–558.
• [6] L. Nachbin, Topology and order. Translated from the Portuguese by Lulu Bechtolsheim. Van Nostrand Mathematical Studies, No. 4 D. Van Nostrand Co., Inc., Princeton, N.J.–Toronto, Ont.–London 1965
• [7] S. Purisch, A History of Results on Orderability and Suborderability. In: Handbook of the History of General Topology. History of Topology, vol 2. (Eds. Aull C.E., Lowen R.) Springer, Dordrecht 1998, pp. 689–702.
• [8] Yu.M. Smirnov, On metrization of topological spaces. Uspehi Mat. Nauk 6 (1951), 100–111.
• [9] J.A. Steebach Jr., L.A. Steen, Counterexamples in Topology. 2nd edition. Springer- Verlag, New York, Heidelberg, Berlin 1978.
• [10] L.A. Steen, A direct proof that a linearly ordered space is hereditarily collectionwise normal. Proc. Amer. Math. Soc. 24 (1970), 727–728.
• [11] S. Willard, General Topology., Addison-Wesley Publishing Company 1970.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).