scholarly journals On spaces with linearlty homeomorphic function spaces in the compact open topology

1998 ◽  
Vol 22 (1) ◽  
pp. 39-48
Author(s):  
Haruto Ohta ◽  
Kohzo Yamada
2001 ◽  
Vol 26 (7) ◽  
pp. 385-392 ◽  
Author(s):  
Koena Rufus Nailana

We determine conditions for quasi-pseudometrizability of the point open ordered spaces and the compact open ordered spaces. This generalizes the results on metrizability of the point open topology and the compact open topology for function spaces. We also study conditions for complete quasi-pseudometrizability.


2003 ◽  
Vol 4 (2) ◽  
pp. 255 ◽  
Author(s):  
Ljubisa D.R. Kocinac

<p>In this paper we investigate some closure properties of the space Ck(X) of continuous real-valued functions on a Tychonoff space X endowed with the compact-open topology.</p>


2011 ◽  
Vol 158 (3) ◽  
pp. 387-391 ◽  
Author(s):  
Gary Gruenhage ◽  
Boaz Tsaban ◽  
Lyubomyr Zdomskyy

1986 ◽  
Vol 100 (2) ◽  
pp. 193-205 ◽  
Author(s):  
John Isbell

The compact–open topology for function spaces is usually attributed to R. H. Fox in 1945 [16]; and indeed, there is no earlier publication to attribute it to. But it is clear from Fox's paper that the idea of the compact–open topology, and its notable success in locally compact spaces, were already familiar. The topology of course goes back to Riemann; and to generalize to locally compact spaces needs only a definition or two. The actual contributions of Fox were (1) to formulate the partial result, and the problem of extending it, clearly and categorically; (2) to show that in separable metric spaces there is no extension beyond locally compact spaces; (3) to anticipate, partially and somewhat awkwardly, the idea of changing the category so as to save the functorial equation. (Scholarly reservations: Fox attributes the question to Hurewicz, and doubtless Hurewicz had a share in (1). As for (2), when Fox's paper was published R. Arens was completing a dissertation which gave a more general result [1] – though worse formulated.)


1999 ◽  
Vol 22 (4) ◽  
pp. 727-737 ◽  
Author(s):  
Gunther Jäger

In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such structures. As a special case, we study a notion of fuzzy compact open topology.


2017 ◽  
Vol 8 (1) ◽  
pp. 31 ◽  
Author(s):  
Ismail Osmano˘glu

In this paper, we introduce (weak) clp-compact-open topology on \(C(X)\) and compare this topology with compact-open topology and the topology of uniform convergence. Then we examine metrizability, completeness and countability properties of the weak clp-compact-open topology on \(C^∗(X)\).


Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4535-4540
Author(s):  
Daniil Lyakhovets ◽  
Alexander Osipov

For a Tychonoff space X, we denote by (C(X), ?k ?p) the bitopological space of all real-valued continuous functions on X, where ?k is the compact-open topology and ?p is the topology of pointwise convergence. In the papers [6, 7, 13] variations of selective separability and tightness in (C(X),?k,?p) were investigated. In this paper we continue to study the selective properties and the corresponding topological games in the space (C(X),?k,?p).


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