H. Tuncali

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20012003

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math.GN2003

Extensional dimension and completion of maps

H. Murat Tuncali, E. D. Tymchatin, Vesko Valov

We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.

math.GN2003

On Regularly Branched Maps

H. Murat Tuncali, Vesko Valov

Let $f : X \to Y$ be a perfect map between finite-dimensional metrizable spaces and $p \geq 1$ . It is shown that the space $C^{*} (X, R^{p})$ of all bounded maps from $X$ into $R^{p}$ …

math.GN2002

On finite-dimensional maps

H. Murat Tuncali, Vesko Valov

Let $f : X \to Y$ be a perfect surjective map of metrizable spaces. It is shown that if $Y$ is a $C$ -space (resp., $dim Y \leq n$ and $dim f \leq m$ ), then the function space $C…

math.GN2002

On finite-to-one maps

H. Murat Tuncali, Vesko Valov

Let $f : X \to Y$ be a $σ$ -perfect $k$ -dimensional surjective map of metrizable spaces such that $dim Y \leq m$ . It is shown that, for every positive integer $p \geq 1$ there exi…

math.GN2002

On Finite-Dimensional Maps II

H. Murat Tuncali, Vesko Valov

Let $f : X \to Y$ be a perfect $n$ -dimensional surjection of paracompact spaces with $Y$ being a $C$ -space. We prove that, for any $m \geq n + 1$ , almost all (in the sense of Baire…

math.GN2001

On dimensionally restricted maps

H. Murat Tuncali, Vesko Valov

Some results of B. Pasynkov and H. Torunczyk on finite-dimensional maps are improved. A generalization of a Dranishnikov-Uspenskij theorem about extensional dimension is also obtai…