English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The space, H(M), of all mappings of the compact manifold M onto itself which can be approximated arbitrarily closely by homeomorphisms is studied. It is shown that H(M) is homogeneous and weakly locally contractible. If M is a compact 2-manifold without boundary, then H(M) is shown to be locally contractible. 1. Let M be a compact manifold and H(M) denote the space of all homeomorphisms of M onto itself. We shall study the space, H(M), of all continuous functions of M onto itself which can be approximated arbitrarily closely by elements of H(M). All function spaces on compact spaces will be assumed to have the supremum metric, p; i.e., if X and V are spaces with d the metric on V and /and g are functions from X into Y, then p(f,g)= supxeX\d(f(x), g(x))l Since M is compact, the topology thus generated agrees with the compact-open topology. A mapping of an n-manifold, Mn, onto itself is said to be cellular if for each y £ M", f~ (y) can be expressed as the intersection of a nested sequence of »cells. Armentrout (» < 3) [4] and Siebenmann (» > 5) [20] have recently shown that H(M"), n /= 4, is precisely the space of all cellular mappings of M" onto itself. Hence most of the results of this paper could be stated in terms of spaces of cellular mappings. Cellular mappings have been studied extensively (cf., Lacher [15], [16]). Let Hd(M) denote the space of all homeomorphisms of M onto itself which equal the identity when restricted to the boundary of M and, following our previous notation, let Hq(M) denote the space of all continuous functions of M onto itself which can be approximated arbitrarily closely by elements of HS(M). We shall state some of the major results concerning 77(M) and H#(M) and then indicate which of the analogous theorems can be proven for 77(M) and H¿(M): Received by the editors December 20, 1972 and, in revised form, July 9, 1973. AMS (MOS) subject classifications (1970). Primary 54H15, 57E05; Secondary 57A60, 57A20.

The closure of the space of homeomorphisms on a manifold. The piecewise linear case