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Research interests

I completed my Ph.D. in 2007 at Lviv National University under the supervision of Dr. Michael Zarichnyi.

The area of my research is in topology and its border with analysis. I am interested in extension of maps, in particular, operators extending families of real-valued functions, (pseudo)metrics and special maps defined on subspaces of topological spaces.

I work on questions of existence and construction of continuous extension operators that preserve properties given on sets of partial maps. In my research I apply techniques and ideas from the theory of continuous selections, measure, hyperspace theory and functional analysis.

Other topics of my scientific interest include continuum theory, aspects of geometric measure theory such as spaces of finite and sigma-finite Hausdorff measure, selection theorems for multi-valued maps and spaces admitting special metrics.

Research statement Publications Conference talks


Publications

1.

Convex metrics on non-compact spaces (with J. Nikiel, M. Tuncali and E.D. Tymchatyn) (submitted) .

2.

Simultaneous brick partitionings of Peano continua (with E.D. Tymchatyn) (preprint) .

3.

Extending functions and metrics with variable domains (with T. Banakh, E.D. Tymchatyn and M. Zarichnyi) (accepted for publication in Topology Appl.) .

4. Spaces of sigma-finite linear measure (with E.D. Tymchatyn) Colloq. Math., 133 (2013), 245-252.
5.

On continuous linear operators extending metrics (with E.D. Tymchatyn) Proc. Amer. Math. Soc. 141 (2013), 2913-2921.

6.

A note on uniformly continuous selections for multi-valued maps (with E.D. Tymchatyn), Topology Proc., 39 (2012), 41-44.

7.

A continuous operator extending fuzzy ultrametrics (with E.D. Tymchatyn), Comment. Math. Univ. Carolin., 52, no. 4 (2011), 611-622.

8.

Extending pairs of metrics (with E.D. Tymchatyn), Mat. Stud. 35, no. 2 (2011), 215-224.

9.

A continuous extension operator for convex metrics (with E.D. Tymchatyn), Canad. Math. Bull. 53 (2010), 719-729.

10.

Continuous linear extension of functions (with A. Koyama, E.D. Tymchatyn and A. Zagorodnyuk), Proc. Amer. Math. Soc. 38 (2010), 4149-4155.

11.

On continuous extension of uniformly continuous functions and metrics (with T. Banakh, N. Brodskiy and E.D. Tymchatyn), Colloq. Math., 116 (2009), 191-202.

12.

A continuous operator extending ultrametrics (with E.D. Tymchatyn) , Comment. Math. Univ. Carolin., 50, no.1 (2009), 141-151.

13.

Spaces of finite Hausdorff measure (with M. Tuncali and E.D. Tymchatyn) (in preparation).

 
14.

Extension of metric structures , PhD thesis, 2007 (in Ukrainian).

15.

Operators extending pseudometrics defined on convex bodies in Euclidean space, Visnyk of Chernivtsi University, Math., 314-315 (2006), 173-180 (in Ukrainian).

 
16.

On operators extending uniformly disconnected metrics , Mat. Stud., 26 (2006), no.1, 101-104.

17.

On operators simultaneously extending partial ultrametrics, Math. Methods and Phys. - Mech. Fields, 49 (2006), no.2, 27-32 (in Ukrainian).

 
18.

Operators extending partial ultrametrics continuous in the topology of pointwise convergence, Visnyk of Lviv University, Series Mech. and Math., 64 (2005), 273-279 (in Ukrainian).

 
19.

Extension of semicontinuous pseudometrics, App. Problems of Mech. and Math., 2 (2004), 88-95 (in Ukrainian).

 
20.

On a homogeneous operator extending partial ultrametrics , Mat. Stud, 22 (2004), no.1, 73-78.


Conference talks

1. I. Stasyuk (with E.D. Tymchatyn), Convex metrics on non-compact spaces , Spring Topology and Dynamic Systems Conference, Jersey City, NJ, USA, 2017.
2. I. Stasyuk (with E.D. Tymchatyn), Simultaneous brick partitionings of Peano continua , Spring Topology and Dynamic Systems Conference, Waco, TX, USA, 2016.
3. I. Stasyuk (with E.D. Tymchatyn), Extensions of convex metrics , Spring Topology and Dynamic Systems Conference, Bowling Green, OH, USA, 2015.
4. I. Stasyuk (with E.D. Tymchatyn), Uniformly continuous selections for multi-valued maps, Spring Topology and Dynamic Systems Conference, Richmond, VA, USA, 2014.
5. I. Stasyuk (with J.Nikiel, M. Tuncali and E.D. Tymchatyn), Convex metrics on non-compact spaces, Spring Topology and Dynamic Systems Conference, New Britain, CT, USA, 2013.
6. I. Stasyuk (with T.Banakh, N. Brodskiy and E.D. Tymchatyn), Extensions of uniformly continuous and Lipschitz functions and metrics, Spring Topology and Dynamic Systems Conference, Mexico City, Mexico, 2012.
7. I. Stasyuk (with M.Tuncali and E.D. Tymchatyn), Spaces of finite Hausdorff measure , Dubrovnik VII, Geometric Topology Conference, Dubrovnik, Croatia, 2011.
8. I. Stasyuk (with E.D. Tymchatyn), A continuous operator extending fuzzy ultrametrics , Spring Topology and Dynamic Systems Conference, Tyler, TX, USA, 2011.
9. I. Stasyuk (with E.D. Tymchatyn), On continuous linear operators extending metrics , Spring Topology and Dynamic Systems Conference, Starkville, MI, USA, 2010.
10. I. Stasyuk (with E.D. Tymchatyn), Uniformly continuous selections for multi-valued maps, Spring Topology and Dynamic Systems Conference, Gainesville, FL, USA, 2009.
11. I. Stasyuk, Extension of uniformly disconnected metrics and ultrametrics, Spring Topology and Dynamic Systems Conference, Milwaukee, WI, USA, 2008.
12. I. Stasyuk, Simultaneous extesion of partial ultrametrics , International Conference ''Analysis and Related Topics'', Lviv, Ukraine, 2005, Book of abstracts, 102.
13. I. Stasyuk, Extending partial pseudometrics in the Euclidean space, Conference devoted to modern problems of Mathematics and Mechanics, Lviv, Ukraine, 2005, Book of abstracts, 252.
14. I.Stasyuk, Extending partial ultrametrics, Conference devoted to modern problems of Mathematics and Mechanics, Lviv, Ukraine, 2004, Book of abstracts, 186-188.
15. I. Stasyuk, Extending pseudometrics defined on closed convex subsets of ${\Bbb R}^n$ , International Conference ''Geometric Topology, Infinite-Dimensional Topology, Absolute Extensors, Applications'', Lviv, Ukraine, 2004, Book of abstracts, P.75-76.