Connected projections of blocking sets of 𝐼ⁿ×𝑀

Rosen, Harvey

doi:10.1090/S0002-9939-1980-0565366-8

Connected projections of blocking sets of $I^{n}\times M$
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by Harvey Rosen

Proc. Amer. Math. Soc. 79 (1980), 335-337

DOI: https://doi.org/10.1090/S0002-9939-1980-0565366-8

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Abstract:

Sufficient conditions are given for each minimal blocking set K of ${I^n} \times M$ to have the closure of its projection, $p(K)$, into ${I^n}$ connected. The construction of some examples of almost continuous functions $f:{I^n} \to M$ in the literature depends on knowing each $\overline {p(K)}$ is connected or perfect.

References

Almost continuous functions

Blocking sets for almost continuous functions

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Kenneth R. Kellum, On a question of Borsuk concerning non-continuous retracts. I, Fund. Math. 87 (1975), 89–92. MR 370527, DOI 10.4064/fm-87-2-89-92
Kenneth R. Kellum, On a question of Borsuk concerning non-continuous retracts. II, Fund. Math. 92 (1976), no. 2, 135–140. MR 420540, DOI 10.4064/fm-92-2-135-140
Kenneth R. Kellum, The equivalence of absolute almost continuous retracts and $\varepsilon$-absolute retracts, Fund. Math. 96 (1977), no. 3, 229–235. MR 514981, DOI 10.4064/fm-96-3-229-235
K. R. Kellum and B. D. Garrett, Almost continuous real functions, Proc. Amer. Math. Soc. 33 (1972), 181–184. MR 293026, DOI 10.1090/S0002-9939-1972-0293026-5
C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744, DOI 10.1007/978-3-642-81735-9
J. Stallings, Fixed point theorems for connectivity maps, Fund. Math. 47 (1959), 249–263. MR 117710, DOI 10.4064/fm-47-3-249-263