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Condensations of Cartesian products

Oleg I. Pavlov (1999)

Commentationes Mathematicae Universitatis Carolinae

We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space X there is a μ such that X μ can be condensed onto a normal ( σ -compact) space if and only if there is no measurable cardinal. For any Tychonoff space X and any cardinal ν there is a Tychonoff space M which preserves many properties of X and such that any one-to-one continuous image of M μ , μ ≤ ν , contains a closed copy...

Condensations of Tychonoff universal topological algebras

Constancio Hernández (2001)

Commentationes Mathematicae Universitatis Carolinae

Let ( L , 𝒯 ) be a Tychonoff (regular) paratopological group or algebra over a field or ring K or a topological semigroup. If nw ( L , 𝒯 ) ≤ τ and nw ( K ) ≤ τ , then there exists a Tychonoff (regular) topology 𝒯 * ⊆ 𝒯 such that w ( L , 𝒯 * ) ≤ τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.

Conditions under which the least compactification of a regular continuous frame is perfect

Dharmanand Baboolal (2012)

Czechoslovak Mathematical Journal

We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the two-point compactification of a locally compact Hausdorff space, and the concept of remainder in a frame compactification. Indeed, one of the characterizations...

Conditions which ensure that a simple map does not raise dimension

W. Dębski, J. Mioduszewski (1992)

Colloquium Mathematicae

The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps...

Conley index for set-valued maps: from theory to computation

Tomasz Kaczynski (1999)

Banach Center Publications

Recent results on the Conley index theory for discrete multi-valued dynamical systems with their consequences for the computation of the index for representable maps are recapitulated. The terminology is simplified with respect to previous presentations, some superfluous hypotheses are abandoned and some conclusions are proved in a simpler way.

Connected economically metrizable spaces

Taras Banakh, Myroslava Vovk, Michał Ryszard Wójcik (2011)

Fundamenta Mathematicae

A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric d X of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set d X ( a , b ) : a , b ∈ A does not exceed the density of A, | d X ( A × A ) | ≤ d e n s ( A ) . The construction of the space X determines a functor : Top...

Currently displaying 1861 – 1880 of 8506