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1. Function spaces on $\tau$-Corson compacta and tightness of polyadic spaces

Creator:
Bell, Murray G. and Marciszewski, W.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
boolean, polyadic, function space, Corson, compact, $C_p (X)$, Eberlein, and tightness
Language:
English
Description:
We apply the general theory of $\tau $-Corson Compact spaces to remove an unnecessary hypothesis of zero-dimensionality from a theorem on polyadic spaces of tightness $\tau $. In particular, we prove that polyadic spaces of countable tightness are Uniform Eberlein compact spaces.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Norm continuity of pointwise quasi-continuous mappings

Creator:
Mirmostafaee, Alireza Kamel
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
function space, weak continuity, generalized continuity, quasi-continuous function, and pointwise topology
Language:
English
Description:
Let X be a Baire space, Y be a compact Hausdorff space and ϕ: X → Cp(Y ) be a quasi-continuous mapping. For a proximal subset H of Y × Y we will use topological games G1(H) and G2(H) on Y × Y between two players to prove that if the first player has a winning strategy in these games, then ϕ is norm continuous on a dense Gδ subset of X. It follows that if Y is Valdivia compact, each quasi-continuous mapping from a Baire space X to Cp(Y ) is norm continuous on a dense Gδ subset of X.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Weak selections and weak orderability of function spaces

Creator:
Gutev, Valentin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Vietoris hyperspace, continuous selection, function space, and weakly orderable space
Language:
English
Description:
It is proved that for a zero-dimensional space $X$, the function space $C_p(X,2)$ has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if $X$ is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space $E$, the function space $C_p(X,E)$ is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial positive answer to a question posed by van Mill and Wattel.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public