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H. Murat Tuncali

Publications and source records attributed to H. Murat Tuncali.

6 recordsLinked to original sources
arXiv2004

On Regularly Branched Maps

Let $f\colon X\to Y$ 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 $\R^p$ with the source limitation topology contains a dense $G_δ$-subset consisting of $f$-regularly branched maps. Here, a map $g\colon X\to\R^p$ is $f$-regularly branched if, for every $n\geq 1$, the dimension of the set $\{z\in Y\times\R^p: |(f\times g)^{-1}(z)|\geq n\}$ is $\leq n\cdot\big(\dim f+\dim Y\big)-(n-1)\cdot\big(p+\dim Y\big)$. This is a parametric version of the Hurewicz theorem on regularly branched maps.

math.GN↗
arXiv2002

On Finite-Dimensional Maps II

Let $f\colon X\to Y$ 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 category) maps $g$ from $X$ into the $m$-dimensional cube have the following property: $g(f^{-1}(y))$ is at most $n$-dimensional for every $y\in Y$.

math.GN↗
arXiv2002

On finite-to-one maps

Let $f\colon X\to Y$ 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 exists a dense $G_δ$-subset ${\mathcal H}(k,m,p)$ of $C(X,\uin^{k+p})$ with the source limitation topology such that if $g\in{\mathcal H}(k,m,p)$, then each fiber of $f\triangle g$ contains at most $\max\{m+k-p+2,1\}$ points.This result provides a proof of two hypotheses of S. Bogatyi, V. Fedorchuk and J. van Mill.

math.GN↗
arXiv2002

On finite-dimensional maps

Let $f\colon X\to Y$ 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 $C(X,\uin^{\infty})$ (resp., $C(X,\uin^{2n+1+m})$) equipped with the source limitation topology contains a dense $G_δ$-set $\mathcal{H}$ such that $f\times g$ embeds $X$ into $Y\times\uin^{\infty}$ (resp., into $Y\times\uin^{2n+1+m}$) for every $g\in\mathcal{H}$. Some applications of this result are also given.

math.GN↗
arXiv2001

On dimensionally restricted maps

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 obtained.

math.GN↗