Mapping theorems on spaces with sn-network g-functions

2015

scientific article

english

- sn-networks
- sn-network g-functions
- g-metrizable spaces
- boundary-compact maps
- sequentially-quotient maps
- pseudo-sequence-covering maps
- sequence-covering maps
- 1-sequence-covering maps

EN
Let Δ be the sets of all topological spaces satisfying the following conditions. (1) Each compact subset of *X* is metrizable; (2) There exists an *sn*-network *g*-function g on *X* such that if *x _{n}* →

*x*and

*y*Є

_{n}*g*(

*n*,

*x*) for all

_{n}*n*Є

*N*, then

*x*is a cluster point of {

*y*}. In this paper, we prove that if

_{n}*X*Є Δ, then each sequentially-quotient boundary-compact map on

*X*is pseudo-sequence-covering; if

*X*Є Δ and

*X*has a point-countable

*sn*-network, then each sequence-covering boundary-compact map on

*X*is 1-sequence-covering. As the applications, we give that each sequentially-quotient boundary-compact map on

*g*-metrizable spaces is pseudo-sequence-covering, and each sequence-covering boundary-compact on

*g*-metrizable spaces is 1-sequence-covering.

199 - 208

CC BY-NC-ND (attribution - noncommercial - no derivatives)

public

10.0

^{}and Poznan Supercomputing and Networking Center

^{}