Abstract
References
- R. Engelking, General Topology, PWN, Warszawa, 1977.
- I. Juhász, K. Kunen and M.E. Rudin, Two More Hereditarily Separable non-Lindelöf spaces, Cand. J. Math. 28, 998-1005, 1976.
- L. Kalantan, Results about $\kappa$-normality, Topology Appl. 125, 47-62, 2002.
- L. Kalantan and M. Saeed, $L$-Normality, Topology Proceedings 50, 141-149, 2017.
- L. Kalantan and P. Szeptycki, $\kappa$-normality and products of ordinals, Topology Appl. 123 (3), 537-545, 2002.
- M.E. Rudin, A Separable Dowker space, Symposia Mathematica, Instituto Nazionale di Alta Mathematica, 1973.
- M.M. Saeed, Countable Normality, J. Math. Anal. 9 (1), 116-123, 2018.
- M.M. Saeed, L. Kalantan and H. Alzumi, $C$ - Paracompactness and $C_2$ - Paracom- pactness, Turk. J. Math. 43, 9-20, 2019.
- E.V. Shchepin, Real Valued Functions and Spaces Close to Normal, Sib. J. Math. 13, 1182-1196, 1972.
- M.K. Singal and A.R. Singal, Mildly Normal Spaces, Kyungpook Math J. 13, 29-31, 1973.
- L. Steen and J.A. Seebach, Counterexamples in Topology, Dover Publications, INC. 1995.
- E.K. van Douwen, The Integers and Topology, in: Handbook of Set-Theoretic Topol- ogy, North-Holland, Amsterdam, 111-167, 1984.
- W. Weiss, Small Dowker Spaces, Pacific J. Math. 94, 485-492, 1981.
Abstract
A topological space $X$ is called $L$-paracompact if there exist a paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f\upharpoonright_{A}:A\longrightarrow f(A)$ is a homeomorphism for each Lindelö}f subspace $A\subseteq X$. A topological space $X$ is called $L_2$-paracompact if there exist a Hausdorff paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f\upharpoonright_{A}:A\longrightarrow f(A)$ is a homeomorphism for each Lindelöf subspace $A\subseteq X$. We investigate these two properties.
Keywords
Lindelöf paracompact countably normal $C$-paracompact $C_2$-paracompact $L$-paracompact $L_2$-paracompact $L$-normal $CP$ $C_2P$
References
- R. Engelking, General Topology, PWN, Warszawa, 1977.
- I. Juhász, K. Kunen and M.E. Rudin, Two More Hereditarily Separable non-Lindelöf spaces, Cand. J. Math. 28, 998-1005, 1976.
- L. Kalantan, Results about $\kappa$-normality, Topology Appl. 125, 47-62, 2002.
- L. Kalantan and M. Saeed, $L$-Normality, Topology Proceedings 50, 141-149, 2017.
- L. Kalantan and P. Szeptycki, $\kappa$-normality and products of ordinals, Topology Appl. 123 (3), 537-545, 2002.
- M.E. Rudin, A Separable Dowker space, Symposia Mathematica, Instituto Nazionale di Alta Mathematica, 1973.
- M.M. Saeed, Countable Normality, J. Math. Anal. 9 (1), 116-123, 2018.
- M.M. Saeed, L. Kalantan and H. Alzumi, $C$ - Paracompactness and $C_2$ - Paracom- pactness, Turk. J. Math. 43, 9-20, 2019.
- E.V. Shchepin, Real Valued Functions and Spaces Close to Normal, Sib. J. Math. 13, 1182-1196, 1972.
- M.K. Singal and A.R. Singal, Mildly Normal Spaces, Kyungpook Math J. 13, 29-31, 1973.
- L. Steen and J.A. Seebach, Counterexamples in Topology, Dover Publications, INC. 1995.
- E.K. van Douwen, The Integers and Topology, in: Handbook of Set-Theoretic Topol- ogy, North-Holland, Amsterdam, 111-167, 1984.
- W. Weiss, Small Dowker Spaces, Pacific J. Math. 94, 485-492, 1981.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 15, 2019 |
| Published in Issue | Year 2019 Volume: 48 Issue: 3 |