Displaying similar documents to “On continuous maps in closure spaces.”

Between closed sets and generalized closed sets in closure spaces

Chawalit Boonpok, Jeeranunt Khampakdee (2008)

Acta Mathematica Universitatis Ostraviensis

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The purpose of the present paper is to define and study ∂ -closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of ∂ -continuous and ∂ -closed maps by using ∂ -closed sets and investigate some of their properties.

κ-compactness, extent and the Lindelöf number in LOTS

David Buhagiar, Emmanuel Chetcuti, Hans Weber (2014)

Open Mathematics

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We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.

A spectral characterization of skeletal maps

Taras Banakh, Andrzej Kucharski, Marta Martynenko (2013)

Open Mathematics

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We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.

A note on the non-emptiness of the limit of approximate systems

Michael G. Charalambous (1996)

Commentationes Mathematicae Universitatis Carolinae

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Short proofs of the fact that the limit space of a non-gauged approximate system of non-empty compact uniform spaces is non-empty and of two related results are given.

Skeletally Dugundji spaces

Andrzej Kucharski, Szymon Plewik, Vesko Valov (2013)

Open Mathematics

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We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with...

Complete ℵ 0 -bounded groups need not be ℝ -factorizable

Mihail G. Tkachenko (2001)

Commentationes Mathematicae Universitatis Carolinae

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We present an example of a complete ℵ 0 -bounded topological group H which is not ℝ -factorizable. In addition, every G δ -set in the group H is open, but H is not Lindelöf.