On some properties of the hyperspace $\theta (X)$ and the study of the space $\downarrow\theta C(X)$
محورهای موضوعی : General topology
R. Sen
1
(Department of Mathematics, Presidency University, 86/1 College Street, Kolkata, India)
کلید واژه: H-closed space, H-set, $theta$-closed set, locally $theta$-$H$ space,
چکیده مقاله :
The aim of the paper is to first investigate some properties of the hyperspace $\theta(X)$, and then in the next article it deals with some detailed study of a special type of subspace $\downarrow\theta C(X)$ of the space $\theta (X\times \mathbb I)$.
[1] R. F. Dickman, J. R. Porter, θ-perfect and θ-absolutely closed functions, IIlinois J. Math. 21 (1977), 42-60.
[2] G. Di Maio, Lj. D. R. Kocinac, Some covering properties of hyperspaces, Topology Appl. 155 (2008), 1959-1969.
[3] J. M. G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472-476.
[4] S. Fomin, Extensions of topological spaces, Ann. Math. 44 (1943), 471-480.
[5] S. Ganguly, S. Jana, R. Sen, A new hyperspace topology and the study of the function space θ∗-LC(X,Y), Mat. Vesnik. 61 (2009), 181-193.
[6] F. Hausdorff, Mengenlehre, 3rd ed., Springer, Berlin, 1927.
[7] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182.
[8] N. V. Velicko, H-closed topological spaces, Amer. Math. Trans. 78 (1968), 103-118.
