A class of topological spaces between the classes of regular and urysohn spaces
-
Dimitrios N. Georgiou
und
Athanasios C. Megaritis
Abstract
The notion of rU-space is given and investigated. A space X is said to be a rU-space if X is a Hausdorff space and for every x ∈ X and every open neighbourhood V of x there exists an open neighbourhood U of x such that U ⊆ Cl(V) and Bd(U) ⊆ V. The class of rU-spaces is properly placed between the classes of regular and Urysohn spaces.
Acknowledgement
The authors would like to thank the referee for the valuable comments and suggestions that improved the quality of the paper.
References
[1] Aull, C. E.: Paracompact subsets. In: 1967 General Topology and its Relations to Modern Analysis and Algebra, II (Proc. Second Prague Topological Sympos., 1966), Academia, Prague, pp. 45–51.10.1016/B978-1-4831-9850-7.50017-5Suche in Google Scholar
[2] Arhangel’skii, A. V.: Relative topological properties and relative topological spaces. In: Proceedings of the International Conference on Convergence Theory (Dijon, 1994), Topology Appl. 70 (1996), pp. 87–99.10.1016/0166-8641(95)00086-0Suche in Google Scholar
[3] Buck, R. E.: Some weaker monotone separation and basis properties, Topology Appl. 69 (1996), 1–12.10.1016/0166-8641(95)00069-0Suche in Google Scholar
[4] Engelking, R.: General Topology. Sigma Ser. Appl. Math. 6, Heldermann Verlag, Berlin, 1989.Suche in Google Scholar
[5] Iliadis, S. D.: Universal Spaces and Mappings. North-Holland Mathematics Studies 198, Elsevier Science B.V., Amsterdam, 2005.Suche in Google Scholar
[6] Miller, G. G.: Countable connected spaces, Proc. Amer. Math. Soc. 26 (1970), 355–360.10.1090/S0002-9939-1970-0263005-0Suche in Google Scholar
[7] Munkres, J. R.: Topology: A First Course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975.Suche in Google Scholar
[8] Ori, R. G.—Rajagopalan, M.: On countable connected locally connected almost regular Urysohn spaces, Topology Appl. 17 (1984), 157–171.10.1016/0166-8641(84)90039-7Suche in Google Scholar
[9] Rosenstein, J. G.: Linear Orderings. Pure Appl. Math. 98, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982.Suche in Google Scholar
[10] Steen, L. A.—Seebach, J. A., Jr.: Counterexamples in Topology, Reprint of the second edition (1978), Dover Publications, Inc., Mineola, NY, 1995.10.1007/978-1-4612-6290-9Suche in Google Scholar
[11] Stone, M. H.: Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375–481.10.1090/S0002-9947-1937-1501905-7Suche in Google Scholar
[12] Thomas, J. P.: Associated regular spaces, Canad. J. Math. 20 (1968), 1087–1092.10.4153/CJM-1968-105-6Suche in Google Scholar
[13] Tzannes, V.: Three countable connected spaces, Colloq. Math. 56 (1988), 267–279.10.4064/cm-56-2-267-279Suche in Google Scholar
[14] Urysohn, P.: Über die Mächtigkeit der zusammenhängenden Mengen, Math. Ann. 94 (1925), 262–295.10.1007/BF01208659Suche in Google Scholar
[15] Willard, S.: General Topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970.Suche in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Cyclic and rotational latin hybrid triple systems
- Notes on mildly distributive semilattices
- On generalized completely distributive posets
- Properties of non-associative MV-algebras
- On the upper and lower exponential density functions
- Quadratic permutations, complete mappings and mutually orthogonal latin squares
- On F-groups with the central factor of order p4
- Comparison of some families of real functions in porosity terms
- Negative interest rates: why and how?
- Homoclinic and heteroclinic motions in hybrid systems with impacts
- Some fixed point theorems in Branciari metric spaces
- S-essential spectra and measure of noncompactness
- Unified approach to graphs and metric spaces
- On structural properties of porouscontinuous functions
- A class of topological spaces between the classes of regular and urysohn spaces
- On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
- Generalized Baskakov type operators
Artikel in diesem Heft
- Cyclic and rotational latin hybrid triple systems
- Notes on mildly distributive semilattices
- On generalized completely distributive posets
- Properties of non-associative MV-algebras
- On the upper and lower exponential density functions
- Quadratic permutations, complete mappings and mutually orthogonal latin squares
- On F-groups with the central factor of order p4
- Comparison of some families of real functions in porosity terms
- Negative interest rates: why and how?
- Homoclinic and heteroclinic motions in hybrid systems with impacts
- Some fixed point theorems in Branciari metric spaces
- S-essential spectra and measure of noncompactness
- Unified approach to graphs and metric spaces
- On structural properties of porouscontinuous functions
- A class of topological spaces between the classes of regular and urysohn spaces
- On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
- Generalized Baskakov type operators
