F-n-resolvable spaces and compactifications
Submitted: 2018-04-25
|Accepted: 2019-02-01
|Published: 2019-04-01
Downloads
Keywords:
categories, functors, resolvable spaces, compactifications
Supporting agencies:
Laboratory of research LATAO (LR11ES12)
Abstract:
A topological space is said to be resolvable if it is a union of
two disjoint dense subsets. More generally it is called n-resolvable if it is a union of n pairwise disjoint dense subsets. In this paper, we characterize topological spaces such that their reflections (resp., compactifications) are n-resolvable (resp., exactly-n-resolvable, strongly-exactly-n-resolvable), for some particular cases of reflections and compactifications.
References:
A. V. Arhangel'skii and A. J. Collins, On submaximal spaces, Topology Appl. 64 (1995), 219-241. https://doi.org/10.1016/0166-8641(94)00093-I
M. Al-Hajri and K. Belaid, Resolvable spaces and compactifications, Advances in Pure Mathematics 3 (2013), 365-367. https://doi.org/10.4236/apm.2013.33052
K. Belaid and L. Dridi, I-spaces, nodec spaces and compactifications, Topology Appl. 161 (2014), 196-205. https://doi.org/10.1016/j.topol.2013.10.021
K. Belaid, O. Echi and S. Lazaar, T(α,β)-space and Wallman compactification, International Journal of Mathematics and Mathematical Sciences 68 (2004), 3717-3735. https://doi.org/10.1155/S0161171204404050
K. Belaid, L. Dridi and O. Echi, Submaximal and door compactifications, Topology Appl. 158 (2011), 1969-1975. https://doi.org/10.1016/j.topol.2011.06.039
J. G. Ceder, On maximally resolvable spaces, Fund. Math. 55 (1964), 87-93. https://doi.org/10.4064/fm-55-1-87-93 https://doi.org/10.4064/fm-55-1-87-93
W. W. Comfort and S. Garc'{i}a-Ferreira, Resolvability: a selective survey and some new results, Topology. Appl. 74 (1996), 149-167. https://doi.org/10.1016/S0166-8641(96)00052-1
I. Dahane, L. Dridi and S. Lazaar, F Resolvable spaces, Math. Appl. 1 (2012), 1-9.
I. Dahane, S. Lazaar, T. Richmond and T. Turki, On resolvable primal spaces, Quaest. Math. 42 (2019), 15-35. https://doi.org/10.2989/16073606.2018.1437093
L. Dridi, S.Lazaar and T. Turki, F-door spaces and F-submaximal spaces, Applied General Topology 14 (2013), 97-113. https://doi.org/10.4995/agt.2013.1621
L. Dridi, A. Mhemdi and T. Turki, F-nodec spaces, Applied General Topology 16 (2015), 53-64. https://doi.org/10.4995/agt.2015.3141
O. Echi and S. Lazaar, Reflective subcategories, Tychonoff spaces, and spectral spaces, Top. Proc. 34 (2009),307-319.
L. Feng, Strongly exactly $n$-resolvable space of arbitrarily large dispersion character, Topology. Appl. 105 (2000), 31-36. https://doi.org/10.1016/S0166-8641(99)00034-6
A. Grothendieck and J. Dieudonné, Eléments de géométrie algébrique, Springer-Verlag, Heidelberg, 1971.
A. Grothendieck and J. Dieudonné, Eléments de géométrie algébrique I: le langage des schemas, Inst. Hautes Etudes Sci. Publ. Math. no. 4, 1960. https://doi.org/10.1007/BF02684778
E. Hewitt, A problem of set theoretic topology, Duke Mathematical Journal 10 (1943), 309-333. https://doi.org/10.1215/S0012-7094-43-01029-4
J. F. Kennisson, The cyclic spectrum of a Boolean flow, Theory Appl. Categ. 10 (2002), 392-409.
J. F. Kennisson, Spectra of finitely generated Boolean flow, Theory Appl. Categ. 16 (2006), 434-459.
M. M. Kovar, Which topological spaces have a weak reflection in compact spaces?, Commentationes Mathematicae Universitatis Carolinae 39 (1938), 529-536.
S. Lazaar, On functionally Hausdorff spaces, Missouri J. Math. Sci. 25 (2013), 88-97.
J. W. Tukey, Convergence and uniformity in topology, Annals of Mathematics Studies, no. 2. Princeton University Press, 1940 Princeton, N. J.
R. C. Walker, The Stone-Cech compactification, Ergebnisse der Mathamatik Band 83.
H. Wallman, Lattices and topological spaces, Ann. Math. 39 (1938), 112-126. https://doi.org/10.2307/1968717
