A class of spaces containing all generalized absolutely closed (almost compact) spaces
The class of θ-compact spaces is introduced which properly contains the class of almost compact (generalized absolutely closed) spaces and is strictly contained in the class of quasicompact spaces. In the realm of almost regular spaces, the class of θ-compact spaces coincides with the class of nearly compact spaces. Moreover, an almost regular θ-compact space is mildly normal (= K-normal). A θ-closed, θ-embedded subset of a θ-compact space is θ-compact and the product of two θ-compact space is θ-compact if one of them is compact. A (strongly) θ-continuous image of a θ-compact space is θ-compact (compact). A space is compact if and only if it is θ-compact and θ-point paracompact.
A. J. D’Aristotle, Quasicompactness and functionally Hausdorff spaces, J. Austral. Math. Soc. 15 (1973), 319–324. http://dx.doi.org/10.1017/S1446788700013239
J. M. Boyte, Point (countable) paracompactness, J. Austral. Math. Soc.,15 (1973), 138–144. http://dx.doi.org/10.1017/S144678870001288X
Á. Császár, General Topology, Adam Higler Ltd, Bristol, 1978.
A. K. Das, A note on θ-Hausdorff spaces, Bull. Cal. Math. Soc. 97(1) (2005), 15–20.
A. S. Davis, Indexed systems of neighbourhoods for general topological spaces, Amer. Math. Monthly 68 (1961), 886–893. http://dx.doi.org/10.2307/2311686
R. F. Dickman and J. R. Porter, θ-perfect and θ-absolutely closed functions, Illinois J. Math. 21 (1977), 42–60.
S. Fomin, Extensions of topological spaces, Ann. Math. 44 (1943), 471–480. http://dx.doi.org/10.2307/1968976
Z. Frolik, Generalizations of compact and Lindelöf spaces, Czechoslovak Math J. 13 (84) (1959), 172–217 (Russian) MR 21 3821.
E. Hewitt, On two problems of Urysohn, Ann. Math. (2) 47 (1946), 503–509. http://dx.doi.org/10.2307/1969089
J. E. Joseph, θ-closure and θ-subclosed graphs, Math. Chron. 8 (1979), 99–117.
J. K. Kohli and A. K. Das, New normality axioms and decompositions of normality,
Glasnik Mat. 37(57)(2002), 163–173.
J. K. Kohli and A. K. Das, On functionally θ-normal spaces, Applied General Topology 6(1) (2005), 1–14.
J. K. Kohli, A. K. Das and R. Kumar, Weakly functionally θ-normal spaces, θ-shrinking of covers and partition of unity, Note di Matematica, 19(2)(1999), 293–297.
C. Kuratowski, Topologie I, Hafner, New York, 1958.
C. T. Liu, Absolutely closed spaces, Trans. Amer. Math. Soc. 130 (1968), 68–104. http://dx.doi.org/10.1090/S0002-9947-1968-0219024-9
T. Noiri, δ-continuous functions, J. Korean Math. Soc. 16 (1980), 161–166.
J. R. Porter and J. Thomas, On H-closed spaces and minimal Hausdorff spaces, Trans. Amer. Math. Soc. 138 (1969), 159–170.
C. T. Scarborough and A. H. Stone, Products of nearly compact spaces, Trans. Amer. Math. Soc. 124 (1966), 131–147. http://dx.doi.org/10.1090/S0002-9947-1966-0203679-7
M. K. Singal and S. P. Arya, On almost regular spaces, Glasnik Mat. 4 (24) (1969), 89–99.
M. K. Singal and S. P. Arya, On almost normal and almost completely regular spaces, Glasnik Mat. 5(25)(1970), 141–152.
M. K. Singal and A. Mathur, On nearly compact spaces, Boll. U.M.I. 2(4) (1969), 702–710.
M. K. Singal and A. R. Singal, Mildly normal spaces, Kyungpook Math. J. 13(1) (1973), 27–31.
S. Sinharoy and B. Bandopadhyay, On θ-completely regular and locally -H closed spaces, Bull. Cal. Math. Soc. 87 (1995), 19–28.
E. V. Stchepin, Real valued functions and spaces close to normal, Sib. J. Math. 13:5 (1972), 1182–1196.
R. M. Stephenson, Jr., Spaces for which the Stone-Weierstrass theorem holds, Trans. Amer. Math. Soc. 133 (1968), 537–546. http://dx.doi.org/10.1090/S0002-9947-1968-0227753-6
R. M. Stephenson, Jr., Product spaces for which Stone-Weierstrass theorem holds, Proc. Amer. Math. Soc. 21 (1969), 284–288. http://dx.doi.org/10.1090/S0002-9939-1969-0250260-8
W. J. Thron, Topological Structures, Holt, Rinehart and Winston, New York (1966).
N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 2, 78 (1968), 103–118.
Metrics powered by PLOS ALM
Cited-By (articles included in Crossref)
This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site
1. Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions
J.K. Kohli, D. Singh, Rajesh Kumar
Applied General Topology vol: 9 issue: 2 first page: 239 year: 2008
Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt