Weakly κ-compact topological spaces
-
David Buhagiar
Abstract
A weaker variant of κ-compactness is introduced and investigated, namely, weak κ-compactness, where κ is a regular uncountable cardinal. It is shown that these two notions coincide when κ is a strongly compact cardinal. The existence of a weakly κ-compact extension for a Tychonoff space is proved. Weak κ-compactness can also be defined by demanding that a certain equivalence holds between certain classes of Baire measures. Finally, κ-measure-compact spaces are introduced and studied.
(Communicated by L'ubica Holá)
References
[1] Alexandroff, A. D.: Additive set-functions in abstract spaces, Mat. Sb. 8(50) (1940), 307-345; 9(51) (1941), 563-625; 13(55) (1943), 169-238.Search in Google Scholar
[2] Buhagiar, D.—Chetcuti, E.: Locally realcompact and HN-complete spaces, Comment. Math. Univ. Carolin. 48(1) (2007), 107-117.Search in Google Scholar
[3] Buhagiar, D.—Chetcuti, E.—Dvurečenskij, A.: Measure-theoretic characterizations of certain topological properties, Bull. Pol. Acad. Sci. Math. 53(1) (2005), 99-109.10.4064/ba53-1-9Search in Google Scholar
[4] Buhagiar, D.—Chetcuti, E.—Weber, H.: Some cardinal functions in lexicographic products of LOTS, Eur. J. Math. 4 (2017), 1505-1514.10.1007/s40879-017-0198-5Search in Google Scholar
[5] Buhagiar, D.—Džamonja, M.: Square compactness and the filter extension property, Fund. Math. 252 (2021), 325-342.10.4064/fm787-4-2020Search in Google Scholar
[6] Dijkstra, J. J.: Measures in Topology, Master Thesis, University of Amsterdam, 1977.Search in Google Scholar
[7] Engelking, R.: General Topology, rev. ed., Heldermann, Berlin, 1989.Search in Google Scholar
[8] Gale, S. L.: Measure-compact spaces, Topology Appl. 45 (1992), 103-118.10.1016/0166-8641(92)90051-ZSearch in Google Scholar
[9] Gillman, L.—Jerison, M.: Rings of Continuous Functions, Springer-Verlag, Berlin, 1976.Search in Google Scholar
[10] Glicksberg, I.: The representation of functionals by integrals, Duke Math. J. 19 (1952), 253-261.10.1215/S0012-7094-52-01926-1Search in Google Scholar
[11] Halmos, P. R.: Measure Theory, Springer-Verlag, New York, 1974.Search in Google Scholar
[12] Herrlich, H.—Van der Slot, J.: Properties which are closely related to compactness, Indag. Math. 29 (1967), 524-529.10.1016/S1385-7258(67)50068-9Search in Google Scholar
[13] Hewitt, E.: Linear functionals on spaces of continuous functions, Fund. Math. 37 (1950), 161-189.10.4064/fm-37-1-161-189Search in Google Scholar
[14] Katětov, M.: Measures in fully normal spaces, Fund. Math. 38 (1951), 73-84.10.4064/fm-38-1-73-84Search in Google Scholar
[15] Kirk, R. B.: Measures in topological spaces and B-compactness, Indag. Math. 31 (1969), 172-183.10.1016/1385-7258(69)90007-9Search in Google Scholar
[16] Knowles, J. D.: Measures on topological spaces, Proc. Lond. Math. Soc. 17(3) (1967), 139-156.10.1112/plms/s3-17.1.139Search in Google Scholar
[17] Moran, W.: The additivity of measures on completely regular spaces, J. Lond. Math. Soc. 43 (1968), 633-639.10.1112/jlms/s1-43.1.633Search in Google Scholar
[18] Moran, W.: Measures and mappings on topological spaces, Proc. Lond. Math. Soc. 19 (1969), 493-508.10.1112/plms/s3-19.3.493Search in Google Scholar
[19] Moran, W.: Measures on metacompact spaces, Proc. Lond. Math. Soc. 20 (1970), 507-524.10.1112/plms/s3-20.3.507Search in Google Scholar
[20] Nagata, J.: Modern General Topology, rev. 2nd ed., Elsevier Science Publishers B. V., Amsterdam, 1985.Search in Google Scholar
[21] Varadarajan, V. S.: Measures on topological spaces, Amer. Math. Soc. Transl. Ser. 2 48 (1965), 161-228.10.1090/trans2/048/10Search in Google Scholar
[22] Woods, R. G.: A Tychonoff almost realcompactification, Proc. Amer. Math. Soc. 43(1) (1974), 200-208.10.2307/2039356Search in Google Scholar
© 2025 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Weak differences, weak BCK-algebras and applications to some partial orders on rings
- Weakly κ-compact topological spaces
- On sharp radius estimates for S*(β) and a product function
- Maximal subextension and stability in m-capacity of maximal subextension of m-subharmonic functions with given boundary values
- Asymptotic behavior of fractional super-linear differential equations
- New and improved oscillation criteria of third-order half-linear delay differential equations via canonical transform
- Global dynamics of the system of difference equations
- Results on oscillatory properties of third-order functional difference equations with semi-canonical operators
- A new approach to metrical fixed point theorems
- Generalized Baker’s result and stability of functional equations using fixed point results
- Characterizations of ℕ-compactness and realcompactness via ultrafilters in the absence of the axiom of choice
- K-theory of oriented flag manifolds
- On certain observations on split continuity and cauchy split continuity
- On the generalized eta- and theta-transformation formulas as the Hecke modular relation
- On some selective star Lindelöf-type properties
Articles in the same Issue
- Weak differences, weak BCK-algebras and applications to some partial orders on rings
- Weakly κ-compact topological spaces
- On sharp radius estimates for S*(β) and a product function
- Maximal subextension and stability in m-capacity of maximal subextension of m-subharmonic functions with given boundary values
- Asymptotic behavior of fractional super-linear differential equations
- New and improved oscillation criteria of third-order half-linear delay differential equations via canonical transform
- Global dynamics of the system of difference equations
- Results on oscillatory properties of third-order functional difference equations with semi-canonical operators
- A new approach to metrical fixed point theorems
- Generalized Baker’s result and stability of functional equations using fixed point results
- Characterizations of ℕ-compactness and realcompactness via ultrafilters in the absence of the axiom of choice
- K-theory of oriented flag manifolds
- On certain observations on split continuity and cauchy split continuity
- On the generalized eta- and theta-transformation formulas as the Hecke modular relation
- On some selective star Lindelöf-type properties
