<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>X</italic> be a locally compact space. A subfamily <italic>ℱ</italic> of the space <italic>D*</italic>(<italic>X</italic>, ℝ) of densely continuous forms with nonempty compact values from <italic>X</italic> to ℝ equipped with the topology <italic>𝒯UC</italic> of uniform convergence on compact sets is compact if and only if {sup(<italic>F</italic>) : <italic>F</italic> ∈ <italic>ℱ</italic>} is compact in the space <italic>Q</italic>(<italic>X</italic>, ℝ) of quasicontinuous functions from <italic>X</italic> to ℝ equipped with the topology <italic>𝒯UC</italic>.</abstract>

Let X be a locally compact space. A subfamily ℱ of the space D*(X, ℝ) of densely continuous forms with nonempty compact values from X to ℝ equipped with the topology 𝒯UC of uniform convergence on compact sets is compact if and only if {sup(F) : F ∈ ℱ} is compact in the space Q(X, ℝ) of quasicontinuous functions from X to ℝ equipped with the topology 𝒯UC.

Quasicontinuous Functions, Densely Continuous Forms and Compactness

Academy of Sciences, Institute of Mathematics

Department of Mathematics and Computer Science, Faculty of Education

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Quasicontinuous Functions, Densely Continuous Forms and Compactness"}

Let X be a locally compact space. A subfamily ℱ of the space D*(X, ℝ) of densely continuous forms with nonempty compact values from X to ℝ equipped with the...

Quasicontinuous Functions, Densely Continuous Forms and Compactness

Published Online: Nov 18, 2017

Page range: 93 - 102

Received: Dec 12, 2016

DOI: https://doi.org/10.1515/tmmp-2017-0008

Keywords
quasicontinuous function, densely continuous form, compactness, densely equi-quasicontinuous, pointwise bounded, boundedly compact metric space

© 2017 L’ubica Holá et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Quasicontinuous Functions, Densely Continuous Forms and Compactness

Published Online: Nov 18, 2017

Page range: 93 - 102

Received: Dec 12, 2016

DOI: https://doi.org/10.1515/tmmp-2017-0008

Keywordsquasicontinuous function, densely continuous form, compactness, densely equi-quasicontinuous, pointwise bounded, boundedly compact metric space

© 2017 L’ubica Holá et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
quasicontinuous function, densely continuous form, compactness, densely equi-quasicontinuous, pointwise bounded, boundedly compact metric space