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Clone properties of topological spaces

Věra Trnková (2006)

Archivum Mathematicum

Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.

Closed discrete subsets of separable spaces and relative versions of normality, countable paracompactness and property ( a )

Samuel Gomes da Silva (2011)

Commentationes Mathematicae Universitatis Carolinae

In this paper we show that a separable space cannot include closed discrete subsets which have the cardinality of the continuum and satisfy relative versions of any of the following topological properties: normality, countable paracompactness and property ( a ) . It follows that it is consistent that closed discrete subsets of a separable space X which are also relatively normal (relatively countably paracompact, relatively ( a ) ) in X are necessarily countable. There are, however, consistent examples of...

Closed embeddings into complements of Σ -products

Aleksander V. Arhangel'skii, Miroslav Hušek (2008)

Commentationes Mathematicae Universitatis Carolinae

In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a Σ -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin axiom and...

Closed graph multi-selections

Valentin Gutev (2011)

Fundamenta Mathematicae

A classical Lefschetz result about point-finite open covers of normal spaces is generalised by showing that every lower semi-continuous mapping from a normal space into the nonempty compact subsets of a metrizable space admits a closed graph multi-selection. Several applications are given as well.

Closed ideals in topological algebras: a characterization of the topological Φ -algebra C k ( X )

F. Montalvo, Antonio A. Pulgarín, Batildo Requejo Fernández (2006)

Czechoslovak Mathematical Journal

Let A be a uniformly closed and locally m-convex Φ -algebra. We obtain internal conditions on A stated in terms of its closed ideals for A to be isomorphic and homeomorphic to C k ( X ) , the Φ -algebra of all the real continuous functions on a normal topological space X endowed with the compact convergence topology.

Closed mapping theorems on k -spaces with point-countable k -networks

Alexander Shibakov (1995)

Commentationes Mathematicae Universitatis Carolinae

We prove some closed mapping theorems on k -spaces with point-countable k -networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space U r with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a k -space X with a point-countable k -network admitting a closed surjection which is not compact-covering contains a closed copy of U r .

Currently displaying 1501 – 1520 of 8504